1,124 research outputs found
Solid hulls and cores of weighted H-infinity-spaces
No full text[EN] We determine the solid hull and solid core of weighted Banach spaces H-upsilon(infinity) of analytic functions functions f such that upsilon vertical bar f vertical bar is bounded, both in the case of the holomorphic functions on the disc and on the whole complex plane, for a very general class of radial weights upsilon. Precise results are presented for concrete weights on the disc that could not be treated before. It is also shown that if H-upsilon(infinity) is solid, then the monomials are an (unconditional) basis of the closure of the polynomials in H-upsilon(infinity). As a consequence H-upsilon(infinity) does not coincide with its solid hull and core in the case of the disc. An example shows that this does not hold for weighted spaces of entire functions.The research of Bonet was partially supported by the project MTM2016-76647-P. The research of Taskinen was partially supported by the Vaisala Foundation of the Finnish Academy of Sciences and Letters.Bonet Solves, JA.; Lusky, W.; Taskinen, J. (2018). Solid hulls and cores of weighted H-infinity-spaces. Revista Matemática Complutense. 31(3):781-804. https://doi.org/10.1007/s13163-018-0265-6S781804313Anderson, J.M., Shields, A.L.: Coefficient multipliers of Bloch functions. Trans. Am. Math. Soc. 224, 255–265 (1976)Bennet, G., Stegenga, D.A., Timoney, R.M.: Coefficients of Bloch and Lipschitz functions. Ill. J. Math. 25, 520–531 (1981)Bierstedt, K.D., Bonet, J., Galbis, A.: Weighted spaces of holomorphic functions on bounded domains. Mich. Math. J. 40, 271–297 (1993)Bierstedt, K.D., Bonet, J., Taskinen, J.: Associated weights and spaces of holomorphic functions. Stud. Math. 127, 137–168 (1998)Blasco, O., Galbis, A.: On Taylor coefficients of entire functions integrable against exponential weights. Math. Nachr. 223, 5–21 (2001)Blasco, O., Pavlovic, M.: Coefficient multipliers on Banach spaces of analytic functions. Rev. Mat. Iberoam. 27, 415–447 (2011)Bonet, J., Taskinen, J.: Solid hulls of weighted Banach spaces of entire functions. Rev. Mat. Iberoam. 34, 593–608 (2018)Bonet, J., Taskinen, J.: Solid hulls of weighted Banach spaces of analytic functions on the unit disc with exponential weights. Ann. Acan. Sci. Fenn. Math. 43, 521–530 (2018)Constantin, O., Peláez, J.A.: Boundedness of the Bergman projection on L p -spaces with exponential weights. Bull. Sci. Math. 139(3), 245–268 (2015)Dostanić, M.R.: Multipliers in the space of analytic functions with exponential mean growth. Asymptot. Anal. 65(3–4), 191–201 (2009)Dostanić, M.-R.: Integration operators on Bergman spaces with exponential weight. Rev. Mat. Iberoam. 23(2), 421–436 (2007)Jevtić, M., Pavlović, M.: On the solid hull of the Hardy-Lorentz space. Publ. Inst. Math. (Beogr.) (N.S.) 85(99), 55–61 (2009)Jevtić, M., Vukotić, D., Arsenović, M.: Taylor Coefficients and Coefficient Multipliers of Hardy and Bergman-Type Spaces. RSME Springer Series, vol. 2. Springer, Berlin (2016)Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces I. Springer, Berlin (1977)Lusky, W.: On the Fourier series of unbounded harmonic functions. J. Lond. Math. Soc. 2(61), 568–580 (2000)Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomorphic functions. Stud. Math. 175, 19–45 (2006)Pau, J., Peláez, J.A.: Volterra type operators on Bergman spaces with exponential weights. Contemp. Math. 561, 239–252. Topics in complex analysis and operator theory. American Mathematical Society, Providence (2012)Pavlović, M.: On harmonic conjugates with exponential mean growth. Czech. Math. J. 49, 733–742 (1999)Pavlović, M.: Function Classes on the Unit Disc: An Introduction. De Gruyter Studies in Mathematics, vol. 52, p. 449. De Gruyter, Berlin (2014)Peláez, J.A., Rättyä, J.: Weighted Bergman Spaces Induced by Rapidly Increasing Weights, vol. 227, no. 1066, pp. vi+124. American Mathematical Society (2014)Shields, A.L., Williams, D.L.: Bounded projections, duality and multipliers in spaces of analytic functions. Trans. Am. Math. Soc. 162, 287–302 (1971
On a problem of topologies in infinite dimensional holomorphy
No full textThe authors solve an interesting open problem concerning the equivalence of the compact-open topology τ0 and the Nachbin ported topology τω on spaces of holomorphic functions. (See, for example, the book by S. Dineen [Complex analysis in locally convex spaces, North-Holland, Amsterdam, 1981; MR0640093 (84b:46050)] for background.) Let H(U) denote the space of complex-valued holomorphic functions on an open subset U of a complex Fréchet-Montel space F. Ansemil and S. Ponte [Arch. Math. (Basel) 51 (1988), no. 1, 65–70; MR0954070 (90a:46109)] showed that these two topologies agree on H(U) for balanced U if and only if, for every natural number n, P(nF) is a Montel space. Using this result, they showed that for balanced open subsets U of certain non-Schwartz, Fréchet-Montel spaces, τ0=τω. Earlier, J. Mujica [J. Funct. Anal. 57 (1984), no. 1, 31–48; MR0744918 (86c:46050)] had shown that τ0=τω for Fréchet-Schwartz spaces. It is not hard to see that the two topologies differ if F is not Montel.
The authors' counterexample is the Fréchet-Montel space F of Taskinen [Studia Math. 91 (1988), no. 1, 17–30; MR0957282 (89k:46087)]. The authors observe that the complete symmetric projective tensor product Fs⊗ˆπF contains an isomorphic copy of l1. Consequently, P(2F) cannot be Montel, and the result follows.Depto. de Análisis Matemático y Matemática AplicadaFac. de Ciencias MatemáticasTRUEpu
Unbounded Bergman projections on weighted spaces with respect to exponential weights
No full text[EN] There are recent results concerning the boundedness and also unboundedness of Bergman projections on weighted spaces of the unit disc in special cases of rapidly decreasing weights, i.e. "large" Bergman spaces. The aim of our paper is to show that the cases of boundedness are largely exceptional: in general the Bergman projections are unbounded. In addition we give a new, more functional analytic proof for the known central boundedness case which also enables us to transfer our results to harmonic Bergman spaces.The research of Bonet was partially supported by the project MCIN PID2020-119457GB-I00/AEI/10.13039/501100011033. The research of Taskinen was partially supported by the Vaisala Foundation of the Finnish Academy of Sciences and Letters.Bonet Solves, JA.; Lusky, W.; Taskinen, J. (2021). Unbounded Bergman projections on weighted spaces with respect to exponential weights. Integral Equations and Operator Theory. 93(6):1-21. https://doi.org/10.1007/s00020-021-02680-2S121936Arroussi, H.: Function and operator theory on large Bergman spaces. Ph.D. thesis, Universitat de Barcelona (2016)Bonet, J., Lusky, W., Taskinen, J.: Solid hulls and cores of weighted -spaces. Rev. Mat. Complut. 31, 781–804 (2018)Bonet, J., Lusky, W., Taskinen, J.: Solid cores and solid hulls of weighted Bergman spaces. Banach J. Math. Anal. 13(2), 468–485 (2019)Constantin, O., Pelaéz, J.: Boundedness of the Bergman projection on -spaces with exponential weights. Bull. Sci. Math. 139, 245–268 (2015)Dostanić, M.: Unboundedness of the Bergman projections on spaces with exponential weights. Proc. Edinb. Math. Soc. 47, 111–117 (2004)Dostanić, M.: Integration operators on Bergman spaces with exponential weight. Rev. Mat. Iberoam. 23, 421–436 (2007)Dostanić, M.: Boundedness of the Bergman projections on -spaces with radial weights. Publ. Inst. Math. (Belgr.) 86, 5–20 (2009)Harutyunyan, A., Lusky, W.: On -subspaces of holomorphic functions. Studia Math. 198, 157–175 (2010)He, Z., Lv, X., Schuster, A.: Bergman spaces with exponential weights. J. Funct. Anal. 276, 1402–1429 (2019)Hedenmalm, H., Korenblum, B., Zhu, K.: Theory of Bergman Spaces, Graduate Texts in Mathematics, vol. 199. Springer, New York (2000)Lusky, W.: On the Fourier series of unbounded harmonic functions. J. Lond. Math. Soc. 61(2), 568–580 (2000)Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomorphic functions. Studia Math. 175, 19–45 (2006)Lusky, W., Taskinen, J.: Bounded holomorphic projections for exponentially decreasing weights. J. Funct. Spaces Appl. 6(1), 59–70 (2008)Pavlović, M.: On harmonic conjugates with exponential mean growth. Czechoslov. Math. J. 49(4), 733–742 (1999)Pavlović, M., Peláez, J.A.: An equivalence for weighted integrals of an analytic function and its derivative. Math. Nachr. 281(11), 1612–1623 (2008)Peláez, J.A., Rättyä, J.: Bergman projection induced by radial weight. Adv. Math. 391, 107950 (2021)Zeytuncu, Y.E.: -regularity of weighted Bergman projections. Trans. Am. Math. Soc. 365, 2959–2976 (2013)Zhu, K.: Operator Theory in Function Spaces, Mathematical Surveys and Monographs, vol. 138, 2nd edn. American Mathematical Society, Providence (2007
Why Is Apolipoprotein CIII Emerging as a Novel Therapeutic Target to Reduce the Burden of Cardiovascular Disease?
No full textApoC-III was discovered almost 50 years ago, but for many years, it did not attract much attention. However, as epidemiological and Mendelian randomization studies have associated apoC-III with low levels of triglycerides and decreased incidence of cardiovascular disease (CVD), it has emerged as a novel and potentially powerful therapeutic approach to managing dyslipidemia and CVD risk. The atherogenicity of apoC-III has been attributed to both direct lipoprotein lipase-mediated mechanisms and indirect mechanisms, such as promoting secretion of triglyceride-rich lipoproteins (TRLs), provoking proinflammatory responses in vascular cells and impairing LPL-independent hepatic clearance of TRL remnants. Encouraging results from clinical trials using antisense oligonucleotide, which selectively inhibits apoC-III, indicate that modulating apoC-III may be a potent therapeutic approach to managing dyslipidemia and cardiovascular disease risk.Peer reviewe
Serum cholesterol levels in neutropenic patients with fever
No full textHypocholesterolemia, which often accompanies infectious diseases has been suggested to serve as a prognostic marker in hospitalized patients. Even though patients with chemotherapyinduced leukopenia are at high risk of infection and mortality, only limited information is available on serum cholesterol levels in these patients. We therefore measured serum cholesterol levels in 17 patients with hematological malignancies during chemotherapyinduced neutropenia and correlated it with clinical outcome. Patients with fever (>38.5 degreesC) showed a significant decrease in serum cholesterol levels within 24 hours. Eight days after onset of the fever nonsurvivors had significantly lower serum cholesterol levels (median 2.09 mmol/l, range 0.492.79, n=6) compared to survivors (median 3.23 mmol/l, range 1.684.86, n=11). Cholesterol levels in survivors returned to baseline levels at the time of discharge from the hospital. At the onset of fever, serum levels of inflammatory cytokines interleukin-6, tumor necrosis factor (TNF) and soluble TNF receptors p55 and p75 were elevated in all patients, but only TNF and TNF receptor p75 levels were significantly different in survivors and nonsurvivors. Our data suggest that a decrease in serum cholesterol levels is a prognostic marker in neutropenic patients with fever. Release of inflammatory cytokines may in part be responsible for hypocholesterolemia in these patients
On boundedness and compactness of Toeplitz operators in weighted H-infinity-spaces
No full text[EN] We characterize the boundedness and compactness of Toeplitz operators T-a with radial symbols a in weighted H-infinity-spaces H(v)(infinity)on the open unit disc of the complex plane. The weights v are also assumed radial and to satisfy the condition (B) introduced by the second named author. The main technique uses Taylor coefficient multipliers, and the results are first proved for them. We formulate a related sufficient condition for the boundedness and compactness of Toeplitz operators in reflexive weighted Bergman spaces on the disc. We also construct a bounded harmonic symbol f such that T-f is not bounded in H-v(infinity) for any v satisfying mild assumptions. As a corollary, the Bergman projection is never bounded with respect to the corresponding weighted sup-norms. However, we also show that, for normal weights v, all Toeplitz operators with a trigonometric polynomial as the symbol are bounded on H-v(infinity) . (C) 2020 Elsevier Inc. All rights reserved.The research of Bonet was partially supported by the projects MTM2016-76647-P and GV Prometeo/2017/102 (Spain). The research of Taskinen was partially supported by a research grant from the Faculty of Science of the University of Helsinki.Bonet Solves, JA.; Lusky, W.; Taskinen, J. (2020). On boundedness and compactness of Toeplitz operators in weighted H-infinity-spaces. Journal of Functional Analysis. 278(10):1-26. https://doi.org/10.1016/j.jfa.2019.108456S12627810Bonet, J., Lusky, W., & Taskinen, J. (2018). Solid hulls and cores of weighted H ∞ -spaces. Revista Matemática Complutense, 31(3), 781-804. doi:10.1007/s13163-018-0265-6Bonet, J., Lusky, W., & Taskinen, J. (2019). Solid cores and solid hulls of weighted Bergman spaces. Banach Journal of Mathematical Analysis, 13(2), 468-485. doi:10.1215/17358787-2018-0049Constantin, O., & Peláez, J. Á. (2015). Boundedness of the Bergman projection on Lp-spaces with exponential weights. Bulletin des Sciences Mathématiques, 139(3), 245-268. doi:10.1016/j.bulsci.2014.08.012Dostanić, M. R. (2004). UNBOUNDEDNESS OF THE BERGMAN PROJECTIONS ON SPACES WITH EXPONENTIAL WEIGHTS. Proceedings of the Edinburgh Mathematical Society, 47(1), 111-117. doi:10.1017/s0013091501000190Engliš, M. (2008). Toeplitz operators and weighted Bergman kernels. Journal of Functional Analysis, 255(6), 1419-1457. doi:10.1016/j.jfa.2008.06.026Grudsky, S., & Vasilevski, N. (2001). Bergman-Toeplitz operators: Radial component influence. Integral Equations and Operator Theory, 40(1), 16-33. doi:10.1007/bf01202952Harutyunyan, A., & Lusky, W. (2010). On L1-subspaces of holomorphic functions. Studia Mathematica, 198(2), 157-175. doi:10.4064/sm198-2-4Luecking, D. H. (1987). Trace ideal criteria for Toeplitz operators. Journal of Functional Analysis, 73(2), 345-368. doi:10.1016/0022-1236(87)90072-3Luecking, D. H. (2007). Finite rank Toeplitz operators on the Bergman space. Proceedings of the American Mathematical Society, 136(05), 1717-1724. doi:10.1090/s0002-9939-07-09119-8Lusky, W. (1995). On Weighted Spaces of Harmonic and Holomorphic Functions. Journal of the London Mathematical Society, 51(2), 309-320. doi:10.1112/jlms/51.2.309Lusky, W. (2006). On the isomorphism classes of weighted spaces of harmonic and holomorphic functions. Studia Mathematica, 175(1), 19-45. doi:10.4064/sm175-1-2Lusky, W., & Taskinen, J. (2008). Bounded holomorphic projections for exponentially decreasing weights. Journal of Function Spaces and Applications, 6(1), 59-70. doi:10.1155/2008/217160Lusky, W., & Taskinen, J. (2011). Toeplitz operators on Bergman spaces and Hardy multipliers. Studia Mathematica, 204(2), 137-154. doi:10.4064/sm204-2-3Mannersalo, P. (2016). Toeplitz operators with locally integrable symbols on Bergman spaces of bounded simply connected domains. Complex Variables and Elliptic Equations, 61(6), 854-874. doi:10.1080/17476933.2015.1120293STROETHOFF, K. (1998). Compact Toeplitz operators on Bergman spaces. Mathematical Proceedings of the Cambridge Philosophical Society, 124(1), 151-160. doi:10.1017/s0305004197002375Taskinen, J., & Virtanen, J. (2010). Toeplitz operators on Bergman spaces with locally integrable symbols. Revista Matemática Iberoamericana, 693-706. doi:10.4171/rmi/614Zorboska, N. (2003). Toeplitz operators with BMO symbols and the Berezin transform. International Journal of Mathematics and Mathematical Sciences, 2003(46), 2929-2945. doi:10.1155/s016117120321203
Monomial basis in Korenblum type spaces of analytic functions
No full text[EN] It is shown that the monomials A = (z(n))(n=0)(infinity) are a Schauder basis of the Frechet spaces A(+)(-gamma), gamma >= 0, that consists of all the analytic functions f on the unit disc such that (1 - vertical bar z vertical bar)(mu)vertical bar f(z)vertical bar is bounded for all mu > gamma. Lusky proved that A is not a Schauder basis for the closure of the polynomials in weighted Banach spaces of analytic functions of type H-infinity. A sequence space representation of the Frechet space A(+)(-gamma) is presented. The case of (LB)-spaces A(-)(-gamma), gamma > 0, that are defined as unions of weighted Banach spaces is also studied.Research of the third author was partially supported by the Vaisala Foundation of the Finnish Academy of Sciences and Letters.Bonet Solves, JA.; Lusky, W.; Taskinen, J. (2018). Monomial basis in Korenblum type spaces of analytic functions. Proceedings of the American Mathematical Society. 146(12):5269-5278. https://doi.org/10.1090/proc/14195S526952781461
A REAL ANALYTICITY RESULT FOR SYMMETRIC FUNCTIONS OF THE EIGENVALUES OF A QUASIPERIODIC SPECTRAL PROBLEM FOR THE DIRICHLET LAPLACIAN
No full textAs is well known, by the Floquet-Bloch theory for periodic problems, one can transform a spectral Laplace-Dirichlet problem in the plane with a set of periodic perforations into a family of “model problems” depending on a parameter n (Formula presented) [0,2π]2 for quasiperiodic functions in the unit cell with a single perforation. We prove real analyticity results for the eigenvalues of the model problems upon perturbation of the shape of the perforation of the unit cell
Penile necrosis in a diabetic with renal disease and clean intermittent catheterization for recurrent urethral stricture
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