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• W1915691172 abstract "In this article, we study the pointwise convergence of the spherical partial integral operator S R f(x) = ∫ B(0,R) f(y)e 2πix.y dy when it is applied to functions with a certain amount of smoothness. In particular, for f ∈ L p α (R n ), n-1/2 < α ≤ n/p, 2 ≤ p < 2n/n-1, we prove that S R f(x) → G α * g(x) C α,p- quasieverywhere on R n , where g ∈ L P (R n ) is such that f = G α * g almost everywhere. A weaker version of this result in the range 0 < α ≤ n-1/2 as well as some related localisation principles are also obtained. For 1 ≤ p < 2 - 1/n and 0 ≤ α < (2-p)n-1/2p, we construct a function f ∈ L p α (R n ) such that S R f(x) diverges everywhere." @default.
• W1915691172 created "2016-06-24" @default.
• W1915691172 creator A5091813147 @default.
• W1915691172 date "2002-11-14" @default.
• W1915691172 modified "2023-10-16" @default.
• W1915691172 title "On the capacity of sets of divergence associated with the spherical partial integral operator" @default.
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• W1915691172 doi "https://doi.org/10.1090/s0002-9947-02-03144-6" @default.
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