On the means of Fourier integrals and Bernstein inequality in the two-weighted setting (Q963670)
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scientific article; zbMATH DE number 5692394
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the means of Fourier integrals and Bernstein inequality in the two-weighted setting |
scientific article; zbMATH DE number 5692394 |
Statements
On the means of Fourier integrals and Bernstein inequality in the two-weighted setting (English)
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13 April 2010
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The authors investigate the norm estimation problem for Cesàro and Abel-Poisson operators acting from \(L_w^p(\mathbb R) \) to \(L_v^q(\mathbb R) \), where \(1<p\leq q<\infty \). These results are extended to the multidimensional case and applied to obtain generalizations of the Bernstein inequality for functions of finite degree of one and several variables.
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\(q\)-condition
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Abel-Poisson mean
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Bernstein inequality
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Cesàro mean
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two-weighted estimates
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