Two-weight L-p-inequalities for dyadic shifts and the dyadic square function

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http://hdl.handle.net/10138/217907

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Vuorinen , E 2017 , ' Two-weight L-p-inequalities for dyadic shifts and the dyadic square function ' , Studia Mathematica , vol. 237 , no. 1 , pp. 25-56 . https://doi.org/10.4064/sm8288-9-2016

Title: Two-weight L-p-inequalities for dyadic shifts and the dyadic square function
Author: Vuorinen, Emil
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2017
Language: eng
Number of pages: 32
Belongs to series: Studia Mathematica
ISSN: 0039-3223
URI: http://hdl.handle.net/10138/217907
Abstract: We consider two-weight L-p -> L-q-inequalities for dyadic shifts and the dyadic square function with general exponents 1 <p, q <infinity. It is shown that if a so-called quadratic A(p,q)-condition related to the measures holds, then a family of dyadic shifts satisfies the two-weight estimate in an R-bounded sense if and only if it satisfies the direct and the dual quadratic testing condition. In the case p = q = 2 this reduces to the result by T. Hytonen, C. Perez, S. Treil and A. Volberg (2014). The dyadic square function satis fi es the two-weight estimate if and only if it satis fi es the quadratic testing condition, and the quadratic A(p,q)-condition holds. Again in the case p = q = 2 we recover the result by F. Nazarov, S. Treil and A. Volberg (1999). An example shows that in general the quadratic A(p,q)-condition is stronger than the Muckenhoupt type A(p,q)-condition.
Subject: dyadic shift
dyadic square function
two-weight inequality
testing condition
REAL VARIABLE CHARACTERIZATION
WELL LOCALIZED OPERATORS
HILBERT TRANSFORM
HAAR MULTIPLIERS
111 Mathematics
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