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Positivity

, Volume 22, Issue 4, pp 1143–1163 | Cite as

Extrapolation results in grand Lebesgue spaces defined on product sets

  • Vakhtang Kokilashvili
  • Alexander Meskhi
Article
  • 53 Downloads

Abstract

Extrapolation results in weighted grand Lebesgue spaces defined with respect to product measure \(\mu \times \nu \) on \(X\times Y\), where \((X, d, \mu )\) and \((Y, \rho , \nu )\) are spaces of homogeneous type, are obtained. As applications of the derived results we prove new one-weight estimates for multiple integral operators such as strong maximal, Calderón–Zygmund and fractional integral operators with product kernels in these spaces.

Keywords

Weighted extrapolation Grand Lebesgue spaces Strong maximal operators Multiple integral operators Calderón–Zygmund operators with product kernels Fractional integrals with product kernels 

Mathematics Subject Classification

46E30 42B20 42B25 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematical Analysis, A. Razmadze Mathematical InstituteI. Javakhishvili Tbilisi State UniversityTbilisiGeorgia
  2. 2.Department of Mathematics, Faculty of Informatics and Control SystemsGeorgian Technical UniversityTbilisiGeorgia

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