69 research outputs found
Orlicz spaces and amenability of hypergroups
No full textIn this note, we introduce and study some generalizations of Reiter's condition (P-p) and their modifications in the context of Orlicz spaces. We use these conditions to study amenability of hypergroups. We end this paper with a result for polynomial hypergroups
Pseudo-differential operators on homogeneous spaces of compact and Hausdorff groups
No full textLet G be a compact Hausdorff group and let H be a closed subgroup of G. We introduce pseudo-differential operators with symbols on the homogeneous space G/H. We present a necessary and sufficient condition on symbols for which these operators are in the class of Hilbert-Schmidt operators. We also give a characterization of and a trace formula for the trace class pseudo-differential operators on the homogeneous space G/H
Lp -Lq boundedness of spectral multipliers of the anharmonic oscillator
No full textIn this note we study the Lp-Lq boundedness of Fourier multipliers of anharmonic oscillators, and as a consequence also of spectral multipliers, for the range 1 < p ≤ 2 ≤ q < ∞. The underlying Fourier analysis is associated with the eigenfunctions of an anharmonic oscillator in some family of differential operators having derivatives of any order. Our analysis relies on a version of the classical Paley-type inequality, introduced by Hörmander, that we extend in our nonharmonic setting.Dans cette note, nous étudions la Lp-Lq continuité des multiplicateurs de Fourier des oscillateurs anharmoniques, et par conséquent des multiplicateurs spectraux également, pour 1 < p ≤ 2 ≤ q < ∞. L’analyse de Fourier sous-jacente est associée aux fonctions propres d’un oscillateur anharmonique dans certaines familles d’opérateurs différentiels ayant des dérivées d’ordre quelconque. Notre analyse s’appuie sur une version de l’inégalité classique de type Paley, introduite par Hörmander, que nous étendons dans notre cadre non harmonique
Análisis multilineal para operadores pseudodiferenciales periódicos y discretos en espacios Lp
No full textEn esta nota anunciamos los resultados de nuestra investigación sobre las propiedades Lp de operadores pseudodiferenciales multilineales periódicos y/o discretos. Primero, revisaremos el análisis multilineal de tales operadores mostrando versiones análogas de los teoremas clásicos disponibles en el análisis multilineal euclidiano (debidos a Coifman y Meyer, Tomita, Miyachi, Fujita, Grafakos, Tao, etc.), pero, en el contexto de operadores periódicos y/o discretos. Se caracterizará la s-nuclearidad, 0 < s ≤ 1, para operadores multilineales pseudodiferenciales periódicos y/o discretos. Para cumplir este objetivo se clasificarán aquellos operadores lineales s-nucleares, 0 < s ≤ 1, multilineales con núcleo, sobre espacios de Lebesgue arbitrarios definidos en espacios de medida σ-finitos. Finalmente, como aplicación de los resultados presentados se obtiene la versión periódica de la desigualdad de Kato-Ponce, y se examina la s-nuclearidad de potenciales de Bessel lineales y multilineales, como también la s-nuclearidad de operadores integrales de Fourier periódicos admitiendo símbolos con tipos adecuados de singularidad.In this note we announce our investigation on the Lp properties for periodic and discrete multilinear pseudo-differential operators. First, we review the periodic analysis of multilinear pseudo-differential operators byshowing classical multilinear Fourier multipliers theorems (proved by Coifman and Meyer, Tomita, Miyachi, Fujita, Grafakos, Tao, etc.) in the context of periodic and discrete multilinear pseudo-differential operators. For this, we use the periodic analysis of pseudo-differential operators developed by Ruzhansky and Turunen. The s-nuclearity, 0 < s ≤ 1, for the discrete and periodic multilinear pseudo-differential operators will be investigated. To do so, we classify those s-nuclear, 0 < s ≤ 1, multilinear integral operators on arbitrary Lebesgue spaces defined on σ-finite measures spaces. Finally, we present some applications of our analysis to deduce the periodic Kato-Ponce inequality and to examine the s-nuclearity of multilinear Bessel potentialsas well as the s-nuclearity of periodic Fourier integral operators admitting suitable types of singularities
Continuity of operators intertwining with translation operators on hypergroups
No full textLet K be a commutative or compact hypergroup. Let m be a bounded complex-valued Borel measure on K, and let T-mu be the corresponding convolution operator of L-1(K). Let S be a bounded linear operator on a Banach space X. We prove that every linear operator Psi:X -> L-1(K) such that Psi S=T-mu Psi is continuous if and only if the pair(S,T mu) has no critical eigenvalues
Ellipticity and Fredholmness of pseudo-differential operators on l(2)(Z(n))
No full textThe minimal operator and the maximal operator of an elliptic pseudo-differential operator with symbols on Z(n) x T-n are proved to coincide and the domain is given in terms of a Sobolev space. Ellipticity and Fredholmness are proved to be equivalent for pseudo-differential operators on Z(n). The index of an elliptic pseudo-differential operator on Z(n) is also computed
The Hausdorff-Young inequality for Orlicz spaces on compact hypergroups
No full textWe prove the classical Hausdorff-Young inequality for the Lebesgue spaces on a compact hypergroup using interpolation of sublinear operators. We use this result to prove the Hausdorff-Young inequality for Orlicz spaces on a compact hypergroup
Hilbert-Schmidt and trace class pseudo-differential operators on the abstract Heisenberg group
No full textLp-Lq multipliers on commutative hypergroups
No full textThe main purpose of this paper is to prove Hormander's L-p-L-q boundedness of Fourier multipliers on commutative hypergroups. We carry out this objective by establishing the Paley inequality and Hausdorff-Young-Paley inequality for commutative hypergroups. We show the L-p-L-q boundedness of the spectral multipliers for the generalised radial Laplacian by examining our results on Chebli-Trimeche hypergroups. As a consequence, we obtain embedding theorems and time asymptotics for the L-p-L-q norms of the heat kernel for generalised radial Laplacian
C*-algebras, H*-algebras and trace ideals of pseudo-differential operators on locally compact, Hausdorff and abelian groups
No full textWe define pseudo-differential operators on a locally compact, Hausdorff and abelian group G as natural extensions of pseudo-differential operators on R-n. In particular, for pseudo-differential operators with symbols in L-2(G x (G) over cap), where (G) over cap is the dual group of G, we give explicit formulas for the products and adjoints, characterize them as Hilbert-Schmidt operators on L-2(G) and prove that they form a C*-algebra, which is also a H*-algebra. We give a characterization of trace class pseudo-differential operators in terms of symbols lying in a subspace of L-1(G x (G) over cap) boolean AND L-2(G x (G) over cap)
- …
