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- W2034731034 abstract "The paper is devoted to the $$d$$ -dimensional extension of the classical identity of Stein and Weiss concerning the action of the Hilbert transform on characteristic functions. Let $$(R_j)_{j=1}^d$$ be the collection of Riesz transforms in $$mathbb{R }^d$$ . For $$1le p<infty $$ , we determine the least constants $$c_{p,d}, C_{p,d}$$ such that $$begin{aligned} int _{mathbb{R }^d} f(x)|R_jf(x)|^ptext{ d }x&le c_{p,d} ||f||_{L^1(mathbb{R }^d)}, int _{mathbb{R }^d} (1-f(x))|R_jf(x)|^ptext{ d }x&le C_{p,d} ||f||_{L^1(mathbb{R }^d)} end{aligned}$$ for any Borel function $$f:mathbb{R }^drightarrow [0,1]$$ . The proof rests on probabilistic methods and the construction of appropriate harmonic functions on $$[0,1]times mathbb{R }$$ ." @default.
- W2034731034 created "2016-06-24" @default.
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- W2034731034 date "2013-08-03" @default.
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- W2034731034 title "On the Action of Riesz Transforms on the Class of Bounded Functions" @default.
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- W2034731034 doi "https://doi.org/10.1007/s11785-013-0323-5" @default.
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