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

2019/07/25 by Álvaro Corvalán, Corvalán, Alvaro, Mario Milman +1
Mathematics · #Advanced Harmonic Analysis Research #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1907.11327

openalex publication_date 2019/07/25 · openalex created_date 2019/08/13 · openalex updated_date 2026/07/28

Abstract

Extending results in \citeM and \citeMM 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. \citekara) for families of functions, that is based on quasi-monotonicity, and use it to provide an index characterization of the RH_p classes, as well as the limiting class RH= RH_LLogL=. \bigcup_p>1RH_p (cf. \citeBMR), which in the abstract case involves extrapolation spaces. Reverse Hölder inequalities associated to L(p,q) norms, and non-doubling measures are also treated.

Citations

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

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