Oscillatory Strongly Singular Integral Associated to the Convex Surfaces of Revolution
Year: 2016
Analysis in Theory and Applications, Vol. 32 (2016), Iss. 4 : pp. 396–404
Abstract
Here we consider the following strongly singular integral TΩ,γ,α,βf(x,t)=∫Rnei|y|−βΩ(y|y|)|y|n+αf(x−y,t−γ(|y|))dy, where Ω∈Lp(Sn−1), p>1, n>1, α>0 and γ is convex on (0,∞).
We prove that there exists A(p,n)>0 such that if β>A(p,n)(1+α), then TΩ,γ,α,β is bounded from L2(Rn+1) to itself and the constant is independent of γ. Furthermore, when Ω∈C∞(Sn−1), we will show that TΩ,γ,α,β is bounded from L2(Rn+1) to itself only if β>2α and the constant is independent of γ.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2016.v32.n4.7
Analysis in Theory and Applications, Vol. 32 (2016), Iss. 4 : pp. 396–404
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: Oscillatory strongly rough singular integral rough kernel surfaces of revolution.