TY  -  
T1  - The Sharp Square Function Estimate with Matrix Weight 
SN  -  /  
UR  - http://hdl.handle.net/10138/312348 
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A1  - Hytonen, Tuomas; Petermichl, Stefanie; Volberg, Alexander 
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PB  -  
Y1  - 2019 
LA  - eng 
AB  - 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.... 
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IS  -  
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OP  -  
KW  - HILBERT TRANSFORM; INEQUALITY; OPERATOR; BOUNDS; NORM; 111 Mathematics 
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ER  -