Singular operators and Fourier multipliers in weighted Lebesgue spaces with variable index |
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Authors: | V M Kokilashvili S G Samko |
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Institution: | (1) Razmadze Mathematical Institute, Academy of Sciences of Georgia, ul. M. Aleksidze 1, Tbilisi, 0193, Georgia;(2) University of Algarve, Campus de Gambelas, Faro, 8000-810, Portugal |
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Abstract: | Mikhlin’s ideas and results related to the theory of spaces L ρ p(·) with nonstandard growth are developed. These spaces are called Lebesgue spaces with variable index; they are used in mechanics, the theory of differential equations, and variational problems. The boundedness of Fourier multipliers and singular operators on the spaces L ρ p(·) are considered. All theorems are derived from an extrapolation theorem due to Rubio de Francia. The considerations essentially use theorems on the boundedness of operators and maximal Hardy-Littlewood functions on Lebesgue spaces with constant index. |
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