Sharp Reverse H\"older property for A_\infty weights on spaces of homogeneous type

By Tuomas Hytönen, C. P'erez, E. Rela. 2012

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In this article we present a new proof of a sharp Reverse Holder Inequality for $A_\infty$ weights that is valid in the context of spaces of homogeneous type. Then we derive two applications: a precise open property of Muckenhoupt classes and, as a consequence of this last result, we obtain a simple proof of a sharp weighted bound for the Hardy-Littlewood maximal function involving $A_\infty$ constants: |M|_{L^p(w)} \leq c (\frac{1}{p-1} [w]_{A_p}[\sigma]_{A_\infty})^{1/p}, where $1<p<\infty$, $\sigma=w^{\frac{1}{1-p}}$ and $c$ depends only on the doubling constant of the measure $\mu$ and the geometric constant $\kappa$ of the quasimetric.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/88582f712d66c4d38e92498163bcaa2a09dbd944

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In Applied Mathematics

Citations in the corpus

Compactness of Riesz transform commutator on stratified Lie groups (2018, background): “For Ap weights on the stratified Lie group (which is an example of spaces of homogeneous type in the sense of Coifman and Weiss [6]) one can refer to [15].”
A sparse domination principle for rough singular integrals (2016, unknown): “A for p=1+ε we obtain |〈TΩf1,f2〉|≤ C ε sup S PSFS;1,1(f1,f2)+Csup S PSFS;1,1(M1+εf1,f2), ε>0. 4 J.M. CONDE-ALONSO, A. CULIUC, F. DI PLINIO, AND Y. OU The above display leads via standard reasoning [9, 17, 28] to the chain of inequalities kTkLt(w)→Lt(w) ≤Ct[w] max © 1, 1 t−1 ª At inf 0<ε<t−1”
Sharp Weighted Bounds for Multilinear Maximal Functions and Calderón–Zygmund Operators (2012, background): “Hytönen and the third author [12] (see also [13] for another proof) showed that (1.”