Matrix weights, Littlewood Paley inequalities and the Riesz transforms

2013/03/28 by Nicholas Boros, Boros, Nicholas, Nikolaos Pattakos +1 · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1303.7180

Abstract

We discuss weighted estimates for the squares of the Riesz transforms, R², on L²(W) where W is a matrix A2 weight. We prove that if W is close to the Identity matrix Id, then the operator norm of R² is close to its unweighted norm on L² which is one. This is done by the use of the Bellman function technique.

Citations

• Heating of the Ahlfors-Beurling operator: weakly quasiregular maps on the plane are quasiregular
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• A dyadic analysis approach to the problem of continuity of weighted\n estimates with respect to the A_p characteristic

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