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Local Hardy spaces on Chébli-Trimèche hypergroups

Walter Bloom, Zengfu Xu (1999)

Studia Mathematica

We investigate the local Hardy spaces h p on Chébli-Trimèche hypergroups, and establish the equivalence of various characterizations of these in terms of maximal functions and atomic decomposition.

Metric unconditionality and Fourier analysis

Stefan Neuwirth (1998)

Studia Mathematica

We investigate several aspects of almost 1-unconditionality. We characterize the metric unconditional approximation property (umap) in terms of “block unconditionality”. Then we focus on translation invariant subspaces L E p ( ) and C E ( ) of functions on the circle and express block unconditionality as arithmetical conditions on E. Our work shows that the spaces p E ( ) , p an even integer, have a singular behaviour from the almost isometric point of view: property (umap) does not interpolate between L E p ( ) and L E p + 2 ( ) . These...

Multiresolution analysis and Radon measures on a locally compact Abelian group

Félix Galindo, Javier Sanz (2001)

Czechoslovak Mathematical Journal

A multiresolution analysis is defined in a class of locally compact abelian groups G . It is shown that the spaces of integrable functions p ( G ) and the complex Radon measures M ( G ) admit a simple characterization in terms of this multiresolution analysis.

Necessary condition for measures which are ( L q , L p ) multipliers

Bérenger Akon Kpata, Ibrahim Fofana, Konin Koua (2009)

Annales mathématiques Blaise Pascal

Let G be a locally compact group and ρ the left Haar measure on G . Given a non-negative Radon measure μ , we establish a necessary condition on the pairs q , p for which μ is a multiplier from L q G , ρ to L p G , ρ . Applied to n , our result is stronger than the necessary condition established by Oberlin in [14] and is closely related to a class of measures defined by Fofana in [7].When G is the circle group, we obtain a generalization of a condition stated by Oberlin [15] and improve on it in some cases.

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