Extrapolation results in grand Lebesgue spaces defined on product sets |
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| Authors: | Vakhtang Kokilashvili Alexander Meskhi |
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| Institution: | 1.Department of Mathematical Analysis, A. Razmadze Mathematical Institute,I. Javakhishvili Tbilisi State University,Tbilisi,Georgia;2.Department of Mathematics, Faculty of Informatics and Control Systems,Georgian Technical University,Tbilisi,Georgia |
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| 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. |
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