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

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http://hdl.handle.net/10138/249340

#### Citation

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 Rights:
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