Two-weight norm inequalities for potential type and maximal operators in a metric space

Details Two-weight norm inequalities for potential type and maximal operators in a metric space Two-weight norm inequalities for potential type and maximal operators in a metric space

2011-05-13

arxiv.org/abs/1105.2661v5

Mathematics

Classical Analysis and ODEs

27 pages, v5 (fixed some techical details; measures allowed with point masses; some imprecise arguments clarified)

Scientific paper

We characterize two-weight norm estimates 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 the non-empty annulus property, which appeared in earlier work on the subject. We further extend the previous Euclidean result by E. T. Sawyer on two-weight norm estimates for fractional maximal functions into spaces of homogeneous type.

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