10,101 research outputs found
About [q]-regularity properties of collections of sets
We examine three primal space local Hoelder type regularity properties of
finite collections of sets, namely, [q]-semiregularity, [q]-subregularity, and
uniform [q]-regularity as well as their quantitative characterizations.
Equivalent metric characterizations of the three mentioned regularity
properties as well as a sufficient condition of [q]-subregularity in terms of
Frechet normals are established. The relationships between [q]-regularity
properties of collections of sets and the corresponding regularity properties
of set-valued mappings are discussed.Comment: arXiv admin note: substantial text overlap with arXiv:1309.700
A two weight local Tb theorem for the Hilbert transform
We obtain a two weight local Tb theorem for any elliptic and gradient
elliptic fractional singular integral operator T on the real line, and any pair
of locally finite positive Borel measures on the line. This includes the
Hilbert transform and in a sense improves on the T1 theorem by the authors and
M. Lacey.Comment: 121 pages, 3 figures, 50 pages of appendices. We correct three gaps
in the treatment of the stopping form in v12: the proof of Lemma 9.3 there
requires a larger size functional, a collection of pairs is missing from the
decomposition at the bottom of page 149, and an error was made in the
definition of restricted norm of a stopping form. Main results unchange
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