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An extension of the Muckenhoupt–Wheeden theorem to generalized weighted Morrey spaces

  • Rza Mustafayev EMAIL logo and Abdulhamit Kucukaslan

Abstract

In this paper, we find the condition on a function ω and a weight v which ensures the equivalency of norms of the Riesz potential and the fractional maximal function in generalized weighted Morrey spaces p,ω(n,v) and generalized weighted central Morrey spaces ˙p,ω(n,v), when v belongs to the Muckenhoupt A-class.

MSC 2010: 42B25; 42B35; 46E30

Award Identifier / Grant number: 1059B191600675-2016-I-2219

Funding statement: The research of Abdulhamit Kucukaslan was totally supported by the grant of The Scientific and Technological Research Council of Turkey (TUBITAK), Grant 1059B191600675-2016-I-2219.

Acknowledgements

We thank the anonymous referee for his/her remarks.

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Received: 2018-07-29
Revised: 2019-03-21
Accepted: 2019-03-25
Published Online: 2020-03-10
Published in Print: 2021-08-01

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