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- W2111720280 abstract "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." @default.
- W2111720280 created "2016-06-24" @default.
- W2111720280 creator A5083120153 @default.
- W2111720280 date "2015-03-01" @default.
- W2111720280 modified "2023-10-18" @default.
- W2111720280 title "Weighted weak-type inequalities for some fractional integral operators" @default.
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- W2111720280 doi "https://doi.org/10.3792/pjaa.91.35" @default.
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