Abstract
Let $p:\R\to(1,\infty)$ be a globally log-H\"older continuous variable exponentand $w:\R\to[0,\infty]$ be a weight. We prove that the Cauchy singular integraloperator $S$ is bounded on the weighted variable Lebesgue space$L^{p(\cdot)}(\R,w)=\{f:fw\in L^{p(\cdot)}(\R)\}$ if and only if the weight $w$satisfies\[\sup_{-\infty<a<b<\infty}\frac{1}{b-a}\|w\chi_{(a,b)}\|_{p(\cdot)}\|w^{-1}\chi_{(a,b)}\|_{p'(\cdot)}<\infty\quad (1/p(x)+1/p'(x)=1).\]
Original language | Unknown |
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Title of host publication | Operator Theory: Advances and Applications |
Pages | 275-291 |
ISBN (Electronic) | 978-3-0348-0648-0 |
DOIs | |
Publication status | Published - 1 Jan 2014 |
Event | Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation. 22nd International Workshop in Operator Theory and its Applications, Sevilla, July 2011 - Duration: 1 Jan 2011 → … |
Conference
Conference | Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation. 22nd International Workshop in Operator Theory and its Applications, Sevilla, July 2011 |
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Period | 1/01/11 → … |