Bounds for the Hilbert Transform with Matrix A2 Weights

Authors

Kelly Bickel, Bucknell UniversityFollow
Brett Wick, Washington University in St. Louis
Stefanie Petermichl, University of Toulouse

Publication Date

2016

Description

Let W denote a matrix A₂ weight. In this paper, we implement a scalar argument using the square function to deduce related bounds for vector-valued functions in L²(W). These results are then used to study the boundedness of the Hilbert transform and Haar multipliers on L²(W). Our proof also shortens the original argument by Treil and Volberg and improves the dependence on the A₂ characteristic.

Journal

Journal of Functional Analysis

Volume

270

Issue

5

First Page

1719

Last Page

1743

Department

Mathematics

Link to Published Version

http://www.sciencedirect.com/science/journal/00221236/270/5

Recommended Citation

Bickel, Kelly; Wick, Brett; and Petermichl, Stefanie. "Bounds for the Hilbert Transform with Matrix A2 Weights." Journal of Functional Analysis (2016) : 1719-1743.