1,721,076 research outputs found
Triangular maximal operators on locally finite trees
Full text linkWe introduce the centred and the uncentred triangular maximal operators mathematical equation and mathematical equation, respectively, on any locally finite tree in which each vertex has at least three neighbours. We prove that both mathematical equation and mathematical equation are bounded on mathematical equation for every mathematical equation in mathematical equation, that mathematical equation is also bounded on mathematical equation, and that mathematical equation is not of weak type (1, 1) on homogeneous trees. Our proof of the mathematical equation boundedness of mathematical equation hinges on the geometric approach of Córdoba and Fefferman. We also establish mathematical equation bounds for some related maximal operators. Our results are in sharp contrast with the fact that the centred and the uncentred Hardy–Littlewood maximal operators (on balls) may be unbounded on mathematical equation for every mathematical equation even on some trees where the number of neighbours is uniformly bounded
Heat Kernel Bounds for Complex Time on Hyperbolic Spaces and Solvable Extensions of H-type Groups
No full textSolvable extensions of H-type groups provide a unified approach to noncompact symmetric spaces of rank one. In this paper we prove optimal pointwise estimates for the heat kernel for complex time p_z. We deduce sharp L^p estimates both for p_z and for the complex heat kernel corresponding to a distinguished right-invariant Laplacian, associated to the Laplace Beltrami operator
Weak type estimates for multiplier operators on noncompact symmetric spaces
No full textIn this paper we prove sharp weak type 1 estimates for spherical Fourier multipliers on symmetric spaces of the noncompact type. Thiscomplements earlier results of J.-Ph. Anker and A.D. Ionescu
On the --boundedness of operators
No full textWe prove that if q is in (1,∞), Y is a Banach space, and T is a linear operator defined on the space of finite linear combinations of (1, q)-atoms in R^n with the property that
sup{TaY : a is a (1, q)-atom} < ∞, then T admits a (unique) continuous extension to a bounded linear operator from H^1(R^n) to Y . We show that the same is true if we replace (1, q)-atoms by continuous (1,∞)-atoms. This is known to be false for (1,∞)-atoms
ZmPIN1-mediated auxin transport is related to cellular differentiation during maize embryogenesis and endosperm development.
No full textTo study the influence of PINFORMED1 (PIN1)-mediated auxin transport during embryogenesis and endosperm development in monocots, the expression pattern of the three identified ZmPIN1 genes was determined at the transcript level. Localization of the corresponding proteins was also analyzed during maize (Zea mays) kernel development. An anti-indole-3-acetic acid (IAA) monoclonal antibody was used to visualize IAA distribution and correlate the direction of auxin active transport, mediated by ZmPIN1 proteins, with the actual amount of auxin present in maize kernels at different developmental stages. ZmPIN1 genes are expressed in the endosperm soon after double fertilization occurs; however, unlike other tissues, the ZmPIN1 proteins were never polarly localized in the plasma membrane of endosperm cells. ZmPIN1 transcripts and proteins also colocalize in developing embryos, and the ZmPIN1 proteins are polarly localized in the embryo cell plasma membrane from the first developmental stages, indicating the existence of ZmPIN1-mediated auxin fluxes. Auxin distribution visualization indicates that the aleurone, the basal endosperm transfer layer, and the embryo-surrounding region accumulate free auxin, which also has a maximum in the kernel maternal chalaza. During embryogenesis, polar auxin transport always correlates with the differentiation of embryo tissues and the definition of the embryo organs. On the basis of these reports and of the observations on tissue differentiation and IAA distribution in defective endosperm-B18 mutant and in N-1-naphthylphthalamic acid-treated kernels, a model for ZmPIN1-mediated transport of auxin and the related auxin fluxes during maize kernel development is proposed. Common features between this model and the model previously proposed for Arabidopsis (Arabidopsis thaliana) are discussed
Estimates for functions of the Laplacian on manifolds with bounded geometry
No full textIn this paper we consider a complete connected noncompact Riemannian manifold M with Ricci curvature bounded from below and positive injectivity radius. Denote by C the Laplace-Beltrami operator on M and by D the operator root L - b, where b denotes the bottom of the spectrum of L. We assume that the kernel associated to the heat semigroup generated by L satisfies a mild decay condition at infinity. We prove that if m, is a bounded, even holomorphic function in a suitable strip of the complex plane, and satisfies Mihlin-Hormander type conditions of appropriate order at infinity, then the operator m(D) extends to an operator of weak type 1.
This partially extends a celebrated result of J. Cheeger, M. Gromov and A Taylor, who proved similar results under much stronger curvature assumptions on M, but without any assumption on the decay of the heat kernel
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