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

2019/10/29 by Javier Duoandikoetxea, Duoandikoetxea, Javier, Marcel Rosenthal +1
Mathematics · #42B25 #42B35 #46E30 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1910.13285

openalex publication_date 2019/10/29 · openalex created_date 2019/11/08 · openalex updated_date 2026/07/28

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|^αw(x) for w∈ 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 Calderón-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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