Convolutions with kernels having singularities on a sphere
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- by Robert S. Strichartz PDF
- Trans. Amer. Math. Soc. 148 (1970), 461-471 Request permission
Abstract:
We prove that convolution with $(1 - |x{|^2})_ + ^{ - \alpha }$ and related convolutions are bounded from ${L^p}$ to ${L^q}$ for certain values of p and q. There is a unique choice of p which maximizes the measure of smoothing $1/p - 1/q$, in contrast with fractional integration where $1/p - 1/q$ is constant. We apply the results to obtain a priori estimates for solutions of the wave equation in which we sacrifice one derivative but gain more smoothing than in Sobolev’s inequality.References
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Additional Information
- © Copyright 1970 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 148 (1970), 461-471
- MSC: Primary 47.70; Secondary 46.00
- DOI: https://doi.org/10.1090/S0002-9947-1970-0256219-1
- MathSciNet review: 0256219