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- W2982636645 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 $win A_p$. 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 Calderon-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." @default.
- W2982636645 created "2019-11-08" @default.
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- W2982636645 date "2019-10-29" @default.
- W2982636645 modified "2023-09-27" @default.
- W2982636645 title "Boundedness of operators on certain power-weighted Morrey spaces beyond the Muckenhoupt weights" @default.
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