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• W2973588081 abstract "Let $mathbb{S}^{d-1}$ denote the unit sphere in Euclidean space $mathbb{R}^d$, $dgeq 2$, equipped with surface measure $sigma_{d-1}$. An instance of our main result concerns the regularity of solutions of the convolution equation [ acdot(fsigma_{d-1})^{ast {(q-1)}}bigvert_{mathbb{S}^{d-1}}=f,text{ a.e. on }mathbb{S}^{d-1}, ] where $ain C^infty(mathbb{S}^{d-1})$, $qgeq 2(d+1)/(d-1)$ is an integer, and the only a priori assumption is $fin L^2(mathbb{S}^{d-1})$. We prove that any such solution belongs to the class $C^infty(mathbb{S}^{d-1})$. In particular, we show that all critical points associated to the sharp form of the corresponding adjoint Fourier restriction inequality on $mathbb{S}^{d-1}$ are $C^infty$-smooth. This extends previous work of Christ & Shao to arbitrary dimensions and general even exponents, and plays a key role in a companion paper." @default.
• W2973588081 created "2019-09-26" @default.
• W2973588081 creator A5050741771 @default.
• W2973588081 creator A5058118854 @default.
• W2973588081 date "2019-09-23" @default.
• W2973588081 modified "2023-09-27" @default.
• W2973588081 title "Smoothness of solutions of a convolution equation of restricted-type on the sphere" @default.
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• W2973588081 hasPublicationYear "2019" @default.
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