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

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

References

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