$B$-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