Generalized local Tb Theorems for Square Functions

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http://hdl.handle.net/10138/312768

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de la Herran , A G & Hofmann , S 2017 , ' Generalized local Tb Theorems for Square Functions ' , Mathematika , vol. 63 , no. 1 , pp. 1-28 . https://doi.org/10.1112/S0025579315000327

Title: Generalized local Tb Theorems for Square Functions
Author: de la Herran, Ana Grau; Hofmann, Steve
Contributor organization: Department of Mathematics and Statistics
Date: 2017-01
Language: eng
Number of pages: 28
Belongs to series: Mathematika
ISSN: 0025-5793
DOI: https://doi.org/10.1112/S0025579315000327
URI: http://hdl.handle.net/10138/312768
Abstract: A local Tb theorem is an L-2 boundedness criterion by which the question of the global behavior of an operator is reduced to its local behavior, acting on a family of test functions b(Q) indexed by the dyadic cubes. We present two versions of such results, in particular, treating square function operators whose kernels do not satisfy the standard Littlewood-Paley pointwise estimates. As an application of one version of the local Tb theorem, we show how the solvability of the Kato problem (which was implicitly based on local Tb theory) may be deduced from this general criterion.
Subject: SINGULAR INTEGRAL-OPERATORS
UNIFORM RECTIFIABILITY
ELLIPTIC-OPERATORS
HARMONIC MEASURE
POISSON KERNELS
T(B) THEOREM
KATO PROBLEM
SPACES
111 Mathematics
Peer reviewed: Yes
Usage restriction: openAccess
Self-archived version: acceptedVersion


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