The Sharp Square Function Estimate with Matrix Weight

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http://hdl.handle.net/10138/312348

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Hytonen , T , Petermichl , S & Volberg , A 2019 , ' The Sharp Square Function Estimate with Matrix Weight ' , Discrete Analysis . https://doi.org/10.19086/da.7597

Title: The Sharp Square Function Estimate with Matrix Weight
Author: Hytonen, Tuomas; Petermichl, Stefanie; Volberg, Alexander
Contributor: University of Helsinki, Tuomas Hytönen / Principal Investigator
Date: 2019-03-28
Language: eng
Number of pages: 8
Belongs to series: Discrete Analysis
ISSN: 2397-3129
URI: http://hdl.handle.net/10138/312348
Abstract: We prove the matrix A(2) conjecture for the dyadic square function, that is, an estimate of the form vertical bar vertical bar S-w vertical bar vertical bar(L2cd(w)-> Lr2) less than or similar to [W](A2), where the focus is on the sharp linear dependence on the matrix A(2) constant. Moreover, we give a mixed estimate in terms of A(2) and A(infinity) constants. The key to the proof is a sparse domination of a process inspired by the integrated form of the matrix-weighted square function.
Subject: HILBERT TRANSFORM
INEQUALITY
OPERATOR
BOUNDS
NORM
111 Mathematics
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