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BOUNDEDNESS OF GENERALIZED RIESZ POTENTIALS ON THE VARIABLE HARDY SPACES

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  14 August 2017

PABLO ROCHA
PABLO ROCHA*
Affiliation:
Universidad Nacional del Sur, INMABB (Conicet), (8000) Bahía Blanca, Buenos Aires, Argentina email pablo.rocha@uns.edu.ar
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Abstract

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We study the boundedness from $H^{p(\cdot )}(\mathbb{R}^{n})$ into $L^{q(\cdot )}(\mathbb{R}^{n})$ of certain generalized Riesz potentials and the boundedness from $H^{p(\cdot )}(\mathbb{R}^{n})$ into $H^{q(\cdot )}(\mathbb{R}^{n})$ of the Riesz potential, both results are achieved via the finite atomic decomposition developed in Cruz-Uribe and Wang [‘Variable Hardy spaces’, Indiana University Mathematics Journal63(2) (2014), 447–493].

Keywords

variable Hardy spacesfractional operators

MSC classification

Primary: 42B25: Maximal functions, Littlewood-Paley theory
Secondary: 42B35: Function spaces arising in harmonic analysis
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 104 , Issue 2 , April 2018 , pp. 255 - 273
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

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