Exact order of the Lebesgue constants of hyperbolic partial sums of multiple Fourier series (Q1085374)
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scientific article; zbMATH DE number 3981770
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Exact order of the Lebesgue constants of hyperbolic partial sums of multiple Fourier series |
scientific article; zbMATH DE number 3981770 |
Statements
Exact order of the Lebesgue constants of hyperbolic partial sums of multiple Fourier series (English)
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1986
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The estimates for the speed of growth of the norms of the operators \(H^ N_{\alpha}: f(x)\to \sum_{| m^{\alpha}| \leq N}c_ m(f)e^{im\cdot x}\) as \(N\to \infty\) and the exact order of the quantity \(\sup_{f}\| f-H^ N_{\alpha}\|\) for the classes of functions having bounded mixed derivative are obtained.
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hyperbolic partial sums of continuous periodic functions of several variables
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functions having bounded mixed derivative
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