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arXiv · 1409.0679

On the boundedness of singular integrals in Morrey spaces and its preduals

Marcel Rosenthal·Hans-Jürgen Schmeisser
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Abstract

We reduce the boundedness of operators in Morrey spaces $L_p^r({\mathbb R}^n)$, its preduals, $H^{\varrho}L_p ({\mathbb R}^n)$, and their preduals $\overset{\circ}{L}{}^r_p({\mathbb R}^n)$ to the boundedness of the appropriate operators in Lebesgue spaces, $L_p({\mathbb R}^n)$. Hereby, we need a weak condition with respect to the operators which is satisfied for a large set of classical operators of harmonic analysis including singular integral operators and the Hardy-Littlewood maximal function. The given vector-valued consideration of these issues is a key ingredient for various applications in harmonic analysis.

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Marcel Rosenthal, Hans-Jürgen Schmeisser. 2014-09-02. On the boundedness of singular integrals in Morrey spaces and its preduals. https://arxiv.org/abs/1409.0679

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