Sharp reverse Hölder inequality for Cp weights and applications
Date
2020Metadata
Show full item recordAbstract
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).