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Net Spaces and Boundedness of Integral Operators

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Abstract

In this paper we introduce new functional spaces which we call net spaces. Using their properties, necessary and sufficient conditions for the integral operators to be of strong or weak type are obtained. Estimates of the norm of the convolution operator in weighted Lebesgue spaces are presented.

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Authors and Affiliations

  1. Gumilyov Eurasian National University, Munatpasova 7, 010010, Astana, Kazakhstan

    Erlan Nursultanov

  2. ICREA and Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C, 08193, Bellaterra (Barcelona), Spain

    Sergey Tikhonov

Authors
  1. Erlan Nursultanov
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  2. Sergey Tikhonov
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Correspondence to Sergey Tikhonov.

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Communicated by Wojciech Czaja.

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Nursultanov, E., Tikhonov, S. Net Spaces and Boundedness of Integral Operators. J Geom Anal 21, 950–981 (2011). https://doi.org/10.1007/s12220-010-9175-7

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  • DOI: https://doi.org/10.1007/s12220-010-9175-7

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