Reverse Hölder Property for Strong Weights and General Measures
نویسندگان
چکیده
We present dimension-free reverse Hölder inequalities for strong Ap weights, 1 ≤ p < ∞. We also provide a proof for the full range of local integrability of A1 weights. The common ingredient is a multidimensional version of Riesz’s “rising sun” lemma. Our results are valid for any nonnegative Radon measure with no atoms. For p =∞, we also provide a reverse Hölder inequality for certain product measures. As a corollary we derive mixed Ap −A∞ weighted estimates.
منابع مشابه
POINTWISE MULTIPLIERS FOR REVERSE HÖLDER SPACES II By
We classify weights which map strong reverse Hölder weight classes to weak reverse Hölder weight spaces under pointwise multiplication.
متن کاملInverse and Reverse 2-facility Location Problems with Equality Measures on a Network
In this paper we consider the inverse and reverse network facility location problems with considering the equity on servers. The inverse facility location with equality measure deals with modifying the weights of vertices with minimum cost, such that the difference between the maximum and minimum weights of clients allocated to the given facilities is minimized. On the other hand, the reverse c...
متن کاملTHE SHARP Ap CONSTANT FOR WEIGHTS IN A REVERSE-HÖLDER CLASS
Coifman and Fefferman established that the class of Muckenhoupt weights is equivalent to the class of weights satisfying the “reverse Hölder inequality”. In a recent paper V. Vasyunin [17] presented a proof of the reverse Hölder inequality with sharp constants for the weights satisfying the usual Muckenhoupt condition. In this paper we present the inverse, that is, we use the Bellman function t...
متن کاملSample Hölder continuity of stochastic processes and majorizing measures
Abstract. We show that for each weakly majorizing measure there is a natural metric with respect to which sample paths of stochastic processes are Hölder continuous and their Hölder norm satisfies a strong integrability condition. We call such metric a minorizing metric. The class of minorizing metrics is minimal among all metrics assuring sample Hölder continuity of processes satisfying certai...
متن کاملIntrinsic Hölder continuity of harmonic functions
In a setting, where only “exit measures” are given, as they are associated with a right continuous strong Markov process on a separable metric space, we provide simple criteria for scaling invariant Hölder continuity of bounded harmonic functions with respect to a distance function which, in applications, may be adapted to the special situation. In particular, already a very weak scaling proper...
متن کامل