\(L^p\) estimates for singular integrals associated to homogeneous surfaces (Q2769329)
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scientific article; zbMATH DE number 1701224
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(L^p\) estimates for singular integrals associated to homogeneous surfaces |
scientific article; zbMATH DE number 1701224 |
Statements
5 February 2002
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boundedness
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singular integral operators
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\(H^1\) kernels
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homogeneous hypersurfaces
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degree of homogeneity
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\(L^p\) estimates for singular integrals associated to homogeneous surfaces (English)
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The authors study singular integral operators with \(H^1\) kernels along homogeneous hypersurfaces \(\{(x,\phi(x)): x\in\mathbb{R}^n\}\). Such operators are shown to be bounded on \(L^p\) spaces if \(\phi|_{\mathbb{S}^{n-1}}\) is real-analytic and the degree of homogeneity is nonzero. A counterexample is given when the degree of homogeneity is zero.
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