Two-weight norm inequalities for potential type and maximal operators in a metric space
Abstract
We characterize two-weight norm inequalities for potential type integral operators in terms of Sawyer-type testing conditions. Our result is stated in a space of homogeneous type with no additional geometric assumptions, such as group structure or non-empty annulus property, which appeared in earlier works on the subject. One of the new ingredients in the proof is the use of a finite collection of adjacent dyadic systems recently constructed by the author and T. Hyt\"onen. We further extend the previous Euclidean characterization of two-weight norm inequalities for fractional maximal functions into spaces of homogeneous type.
Keywords
Cite
@article{arxiv.1105.2661,
title = {Two-weight norm inequalities for potential type and maximal operators in a metric space},
author = {Anna Kairema},
journal= {arXiv preprint arXiv:1105.2661},
year = {2013}
}
Comments
33 pages, v8 (some typos corrected; clarified the relationship between the different constants present in the several steps of the proof of the main result; Lemma 6.18 modified; examples of spaces and operators included; fixed some technical details; Definition 2.14 and Lemma 2.15 modified; Lemma 6.17 corrected; measures allowed with point masses; some imprecise arguments clarified)