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

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#### Pysyväisosoite

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

#### Lähdeviite

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

 Julkaisun nimi: Boundedness of non-homogeneous square functions and Lq type testing conditions with $q \in (1,2)$ Tekijä: Martikainen, Henri; Mourgoglou, Mihalis Tekijän organisaatio: Department of Mathematics and Statistics Päiväys: 2015 Kieli: eng Sivumäärä: 41 Kuuluu julkaisusarjaan: Mathematical Research Letters ISSN: 1073-2780 DOI-tunniste: https://doi.org/10.4310/MRL.2015.v22.n5.a8 URI: http://hdl.handle.net/10138/249340 Tiivistelmä: 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.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.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. Avainsanat: 111 Mathematics Vertaisarvioitu: Kyllä Tekijänoikeustiedot: cc_by_nc Pääsyrajoitteet: closedAccess Rinnakkaistallennettu versio: submittedVersion Rahoittaja: Academy of Finland Rahoitusnumero: 266262
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