期刊论文详细信息
Proceedings of the Japan Academy, Series A. Mathematical Sciences | |
Weighted weak-type inequalities for some fractional integral operators | |
article | |
Adam Osȩkowski1  | |
[1]Faculty of Mathematics, University of Warsaw | |
关键词: Fractional integral; weight; Muckenhoupt-Wheeden conjecture; best constant.; | |
DOI : 10.3792/pjaa.91.35 | |
学科分类:数学(综合) | |
来源: Japan Academy | |
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【 摘 要 】
For $0<\alpha<1$, let $W_{\alpha}$ and $R_{\alpha}$ denote Weyl fractional integral operator and Riemann-Liouville fractional integral operator, respectively. We establish sharp versions of Muckenhoupt-Wheeden conjecture for these operators. Specifically, we prove that for any weight $w$ on $[0,\infty)$, we have \begin{equation*} \|{W}_{α} f\|_{L^{1/(1-α),∞}(w)}≤ α^{-1}\|{f}\|_{L^{1}((M_{-}w)^{1-α})} \end{equation*} and \begin{equation*} \|{R}_{α} f\|_{L^{1/(1-α),∞}(w)}≤ α^{-1}\|{f}\|_{L^{1}((M_{+}w)^{1-α})}. \end{equation*} Here $M_{-}$, $M_{+}$ denote the one-sided Hardy-Littlewood maximal operators on $[0,\infty)$. In each of the estimates, the constant $\alpha^{-1}$ is the best possible.【 授权许可】
Unknown
【 预 览 】
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