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- W1520234340 abstract "This paper is concerned with singular convolution operators in $mathbb {R}^{d}$, $dge 2$, with convolution kernels supported on radial surfaces $y_{d}=Gamma (|yâ|)$. We show that if $Gamma (s)=log s$, then $L^{p}$ boundedness holds if and only if $p=2$. This statement can be reduced to a similar statement about the multiplier $m(tau ,eta )=|tau |^{-ieta }$ in $mathbb {R}^{2}$. We also construct smooth $Gamma$ for which the corresponding operators are bounded for $p_{0}<ple 2$ but unbounded for $ple p_{0}$, for given $p_{0}in [1,2)$. Finally we discuss some examples of singular integrals along convex curves in the plane, with odd extensions." @default.
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- W1520234340 date "1999-05-20" @default.
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- W1520234340 title "Classes of singular integrals along curves and surfaces" @default.
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- W1520234340 doi "https://doi.org/10.1090/s0002-9947-99-02496-4" @default.
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