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Calderón–Zygmund Type Singular Operators in Weighted Generalized Morrey Spaces

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Abstract

We find conditions for the weighted boundedness of a general class of multidimensional singular integral operators in generalized Morrey spaces \(\mathcal {L}^{p,\varphi }(\mathbb {R}^n,w),\) defined by a function \(\varphi (x,r)\) and radial type weight \(w(|x-x_0|), x_0\in {\mathbb {R}}^{n}.\) These conditions are given in terms of inclusion into \(\mathcal {L}^{p,\varphi }(\mathbb {R}^n,w),\) of a certain integral constructions defined by \(\varphi \) and w. In the case of \(\varphi =\varphi (r)\) we also provide easy to check sufficient conditions for that in terms of indices of \(\varphi \) and w.

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Authors and Affiliations

  1. Luleå University of Technology, Luleå, Sweden

    Lars-Erik Persson, Natasha Samko & Peter Wall

  2. Narvik University College, Narvik, Norway

    Lars-Erik Persson

Authors
  1. Lars-Erik Persson
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  2. Natasha Samko
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  3. Peter Wall
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Correspondence to Natasha Samko.

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Communicated by Hans G. Feichtinger.

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Persson, LE., Samko, N. & Wall, P. Calderón–Zygmund Type Singular Operators in Weighted Generalized Morrey Spaces. J Fourier Anal Appl 22, 413–426 (2016). https://doi.org/10.1007/s00041-015-9418-x

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  • DOI: https://doi.org/10.1007/s00041-015-9418-x

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