On convolution operators in the spaces of almost periodic functions and \(L^p\) spaces (Q1578904)
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scientific article; zbMATH DE number 1501861
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On convolution operators in the spaces of almost periodic functions and \(L^p\) spaces |
scientific article; zbMATH DE number 1501861 |
Statements
On convolution operators in the spaces of almost periodic functions and \(L^p\) spaces (English)
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16 November 2000
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The authors consider convolution operators generated by \(L^1\) functions in \(L^p\) spaces and in the spaces of Bohr, Stepanov and Besicovich of almost periodic functions. They prove that if such an operator is invertible in one of these spaces, then it is invertible in all the spaces. Next, they also prove that convolution operators have identical norms in each of two members of the couples: \(L^p\) and \(B^p\), \(BS^p\) and \(S^p\), \(C_b\) and CAP.
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convolution operators
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spaces of Bohr, Stepanov and Besicovich of almost periodic functions
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