$B$-Riesz Transforms Generated by Generalized Translate Operator on $HM^p_{q,{\Delta_{\nu}}}$ Hardy-Morrey Spaces

Year 2022, Volume: 5 Issue: 2, 127 - 134, 01.06.2022

Cansu Keskin

https://doi.org/10.33401/fujma.1013757

https://izlik.org/JA57NX74XH

Abstract

We study the decomposition of Hardy-Morrey spaces via atoms and molecules, which have similar properties of $H^{p}_{\Delta_{\nu}}(\mathbb{R}^{n}_{+})$ Hardy spaces. Then we introduce the $HM^p_{q,{\Delta_{\nu}}}$ boundedness of $ B $-Riesz transforms generated by a generalized translate operator that is associated to Laplace Bessel operator for $0<p\leq 1<q\leq \infty$ with $p\neq q$ through atomic decomposition and molecular characterization.

Keywords

$B$-Riesz transforms , Decomposition theory , Generalized translation operator , Hardy-Morrey spaces , Laplace-Bessel differential operator

Supporting Institution

TUBITAK

Project Number

119N455

Thanks

The author would like to express their sincere thanks to the editor and the anonymous reviewers for their helpful comments and suggestions.

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