\(L^p\)-\(L^q\) estimates for convolution operators with \(n\)-dimensional singular measures (Q1370730)
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scientific article; zbMATH DE number 1079114
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(L^p\)-\(L^q\) estimates for convolution operators with \(n\)-dimensional singular measures |
scientific article; zbMATH DE number 1079114 |
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\(L^p\)-\(L^q\) estimates for convolution operators with \(n\)-dimensional singular measures (English)
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13 December 1999
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Let \(d\sigma\) denote a compactly supported smooth density on the graph \(x_{n+1}= \sum^n_{j=1}| x_j|^{a_j}\), here \(a_j>0\). The authors prove nearly sharp \(L^p\)-\(L^q\) estimates for the convolution \(d\sigma* f\). For endpoint results see the authors' paper [Colloq. Math. 76, No. 1, 35-47 (1998; Zbl 0915.42009)].
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singular measures
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\(L^p\)-\(L^q\) estimates
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convolution
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