On \(L_p\)-\(L_q\) boundedness for convolutions with kernels having singularities on a sphere (Q2717551)
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scientific article; zbMATH DE number 1605150
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On \(L_p\)-\(L_q\) boundedness for convolutions with kernels having singularities on a sphere |
scientific article; zbMATH DE number 1605150 |
Statements
17 June 2001
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convolution
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multiplier
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singular integral
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\(L_p\) space
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On \(L_p\)-\(L_q\) boundedness for convolutions with kernels having singularities on a sphere (English)
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Author's smmary: ``For the convolution operators \(A^\alpha_a\) with symbols \(a(|\xi|)|\xi|^{-\alpha}\exp i|\xi|\), \(0\leq \Re \alpha < n\), \(a(|\xi|)\in L_\infty\), we construct integral representations and give the exact description of the set of pairs \((1/p,1/q)\) for which the operators are bounded from \(L_p\) to \(L_q\)''.
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