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BOUNDEDNESS OF GENERALIZED RIESZ POTENTIALS ON THE VARIABLE HARDY SPACES
Part of
- Harmonic analysis in several variables
PABLO ROCHA
Journal:

Journal of the Australian Mathematical Society / Volume 104 / Issue 2 / April 2018

Published online by Cambridge University Press:

14 August 2017, pp. 255-273

Print publication:

April 2018
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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].