On the strong differentiation of integrals of functions from Hölder classes (Q1897220)
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scientific article; zbMATH DE number 796768
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the strong differentiation of integrals of functions from Hölder classes |
scientific article; zbMATH DE number 796768 |
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On the strong differentiation of integrals of functions from Hölder classes (English)
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24 September 1995
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The author considers problems of strong differentiability of multiple integrals of functions from the Hölder class \(H_1^{\omega_1, \ldots, \omega_N}\). Among others, he proves the following: (i) in the isotropic case, the conditions of differentiability do not differ from the condition of the embedding into the class \(L (\log^+ L)^{N - 1}\); (ii) in the anisotropic case, this is no longer true. Some application to multiple Fourier series is also included.
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strong differentiability
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multiple integrals
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Hölder class
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multiple Fourier series
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