Sharp reverse Hölder inequality for Cp weights and applications
We prove an appropriate sharp quantitative reverse Hölder inequality for the $C_p$ class of weights fromwhich we obtain as a limiting case the sharp reverse Hölder inequality for the $A_\infty$ class of weights (Hytönen in Anal PDE 6:777–818, 2013; Hytönen in J Funct Anal 12:3883–3899, 2012). We use...
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| Tipo de documento: | artigo |
| Estado: | Versión aceptada para publicación |
| Data de publicação: | 2020 |
| País: | España |
| Recursos: | Basque Center for Applied Mathematics (BCAM) |
| Repositório: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/1107 |
| Acesso em linha: | http://hdl.handle.net/20.500.11824/1107 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Weighted inequalities $A_\infty$ $C_p$ Calderón-Zygmund operator Hardy-Littelwood maximal operator |
| Resumo: | We prove an appropriate sharp quantitative reverse Hölder inequality for the $C_p$ class of weights fromwhich we obtain as a limiting case the sharp reverse Hölder inequality for the $A_\infty$ class of weights (Hytönen in Anal PDE 6:777–818, 2013; Hytönen in J Funct Anal 12:3883–3899, 2012). We use this result to provide a quantitative weighted norm inequality between Calderón–Zygmund operators and theHardy–Littlewood maximal function, precisely $$|| T f ||_{ L^p(w)} \leq C_{T,n,p,q} [w]_{C_q} (1 + \log^+[w]_{C_q} ) ||Mf ||_{ L^p(w)} ,$$ for $w ∈ C_q$ and $q > p > 1$, quantifying Sawyer’s theorem (StudMath 75(3):753–763, 1983). |
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