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arXiv · 2110.14259

Singular and fractional integral operators on weighted local Morrey spaces

Javier Duoandikoetxea·Marcel Rosenthal
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Abstract

We obtain a characterization of the weighted inequalities for the Riesz transforms on weighted local Morrey spaces. The condition is sufficient for the boundedness on the same spaces of all Calder\'on-Zygmund operators suitably defined on the functions of the space. In the case of the fractional maximal operator and the fractional integral we obtain a characterization valid for exponents satisfying the Sobolev relation. For power weights we get sharp results in a larger range of exponents for the usual versions of weighted Morrey spaces.

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Javier Duoandikoetxea, Marcel Rosenthal. 2021-10-27. Singular and fractional integral operators on weighted local Morrey spaces. https://arxiv.org/abs/2110.14259

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