A note on the theorems of Paley and Stein (Q2730508)
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scientific article; zbMATH DE number 1631379
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the theorems of Paley and Stein |
scientific article; zbMATH DE number 1631379 |
Statements
8 August 2001
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Lorentz space
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BMO
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Fourier coefficients
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Lorentz norm
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A note on the theorems of Paley and Stein (English)
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The author gives an estimate of the Lorentz norm of a function in terms of its Fourier coefficients with respect to an orthonormal system \(\{\varphi_n\}\) on \([0,1 ]\), where \(\varphi_n\in\text{BMO}\), and the BMO-seminorm \(\|\varphi_n\|_*\) is bounded. The results generalize the classical theorems by Paley and Stein, and also refine the estimates proposed by \textit{V. I. Kolyada} [Math. Notes, 51, No. 3, 235-244 (1992); translation from Mat. Zametki 51, No. 3, 24-34 (1992; Zbl 0791.42019)].
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