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arXiv · 1910.13285

Boundedness of operators on certain power-weighted Morrey spaces beyond the Muckenhoupt weights

Javier Duoandikoetxea·Marcel Rosenthal
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Abstract

We prove that for operators satistying weighted inequalities with $A_p$ weights the boundedness on a certain class of Morrey spaces holds with weights of the form $|x|^\alpha w(x)$ for $w\in A_p$. In the case of power weights the shift with respect to the range of Muckenhoupt weights was observed by N.~Samko for the Hilbert transform, by H.~Tanaka for the Hardy-Littlewood maximal operator, and by S.~Nakamura and Y.~Sawano for Calder\'on-Zygmund operators and others. We extend the class of weights and establish the results in a very general setting, with applications to many operators. For weak type Morrey spaces, we obtain new estimates even for the Hardy-Littlewood maximal operator. Moreover, we prove the necessity of certain $A_q$ condition.

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BibTeXRIS

Javier Duoandikoetxea, Marcel Rosenthal. 2019-10-29. Boundedness of operators on certain power-weighted Morrey spaces beyond the Muckenhoupt weights. https://arxiv.org/abs/1910.13285

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