Reverse Holder inequalities revisited: Interpolation, Extrapolation, Indices and Doubling

Abstract

Extending results in \cite{M} and \cite{MM} we characterize the classical classes of weights that satisfy reverse Hölder inequalities in terms of indices of suitable families of $K-$functionals of the weights. In particular, we introduce a Samko type of index (cf. \cite{kara}) for families of functions, that is based on quasi-monotonicity, and use it to provide an index characterization of the $R{H}_p$ classes, as well as the limiting class $RH=$ $R{H}_{LLogL}=$. $\bigcup _{p>1}R{H}_p$ (cf. \cite{BMR}),\ which in the abstract case involves extrapolation spaces. Reverse Hölder inequalities associated to $L(p,q)$ norms, and non-doubling measures are also treated.

38 pages

References in corpus (1)

• Non-divergence Parabolic Equations of Second Order with Critical Drift in Lebesgue Spaces