The Hardy-Littlewood theorem for double Fourier-Haar series from mixed metric Lebesgue \(L_{\bar p}[0, 1]^2\) and net \(N_{\bar p,\bar q}(M)\) spaces (Q2116385)
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scientific article; zbMATH DE number 7491535
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Hardy-Littlewood theorem for double Fourier-Haar series from mixed metric Lebesgue \(L_{\bar p}[0, 1]^2\) and net \(N_{\bar p,\bar q}(M)\) spaces |
scientific article; zbMATH DE number 7491535 |
Statements
The Hardy-Littlewood theorem for double Fourier-Haar series from mixed metric Lebesgue \(L_{\bar p}[0, 1]^2\) and net \(N_{\bar p,\bar q}(M)\) spaces (English)
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16 March 2022
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This paper is one of the numerous ones where interactions between integrability and structural properties of functions and summability properties of its Fourier coefficients are studied. Transference of the study of the Hardy-Littlewood theorem from the trigonometric case to the case of the Fourier-Haar coefficients is a known topic. What is specific in the paper under review is not the multivariate (double to be precise) setting but obtaining the Hardy-Littlewood theorem in Lebesgue spaces with mixed metric and in anisotropic net spaces.
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net space
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Lebesgue space
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anisotropic space
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Fourier series
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Haar system
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