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

 dc.contributor.author Martikainen, Henri dc.contributor.author Mourgoglou, Mihalis dc.date.accessioned 2018-10-12T10:52:01Z dc.date.available 2018-10-12T10:52:01Z dc.date.issued 2015 dc.identifier.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 dc.identifier.other PURE: 61081308 dc.identifier.other PURE UUID: 561903ba-2860-4b42-a86d-7e284c8d8aa9 dc.identifier.other Scopus: 84964989071 dc.identifier.other WOS: 000432789400008 dc.identifier.uri http://hdl.handle.net/10138/249340 dc.description.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. sv dc.description.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. fi dc.description.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. en dc.format.extent 41 dc.language.iso eng dc.relation.ispartof Mathematical Research Letters dc.rights cc_by_nc dc.rights.uri info:eu-repo/semantics/closedAccess dc.subject 111 Mathematics dc.title Boundedness of non-homogeneous square functions and Lq type testing conditions with $q \in (1,2)$ en dc.type Article dc.contributor.organization Department of Mathematics and Statistics dc.description.reviewstatus Peer reviewed dc.relation.doi https://doi.org/10.4310/MRL.2015.v22.n5.a8 dc.relation.issn 1073-2780 dc.rights.accesslevel closedAccess dc.type.version submittedVersion dc.relation.funder Academy of Finland dc.relation.grantnumber 266262