Boundedness of non-homogeneous square functions and Lq type testing conditions with $q \in (1,2)$

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Martikainen , H & Mourgoglou , M 2015 , ' Boundedness of non-homogeneous square functions and Lq type testing conditions with $q \in (1,2)$ ' , Mathematical Research Letters , vol. 22 , no. 5 , pp. 1417-1457 . https://doi.org/10.4310/MRL.2015.v22.n5.a8

Title: Boundedness of non-homogeneous square functions and Lq type testing conditions with $q \in (1,2)$
Author: Martikainen, Henri; Mourgoglou, Mihalis
Other contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2015
Language: eng
Number of pages: 41
Belongs to series: Mathematical Research Letters
ISSN: 1073-2780
DOI: https://doi.org/10.4310/MRL.2015.v22.n5.a8
URI: http://hdl.handle.net/10138/249340
Abstract: We continue the study of local Tb theorems for square functions defined in the upper half-space (R-+(n+1), mu x dt/t). Here mu is allowed to be a non-homogeneous measure in R-n. In this paper we prove a boundedness result assuming local L-q type testing conditions in the difficult range q is an element of (1, 2). Our theorem is a non-homogeneous version of a result of S. Hofmann valid for the Lebesgue measure. It is also an extension of the recent results of M. Lacey and the first named author where non-homogeneous local L-2 testing conditions have been considered.
Subject: 111 Mathematics
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