Sharp Bounds for Calderón-Zygmund Operators in a Vector-Valued Setting

Författare: Andrei Stoica; Matematik (naturvetenskapliga Fakulteten); []

Nyckelord: NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Calderón-Zygmund operator; martingale transform; Bellman function; dyadic Haar shift; UMD space; matrix A2 weight; weighted L2-space; Carleson embedding theorem;

Sammanfattning: In this thesis we extend several classical results about Calderón-Zygmund operators to spaces of vector-valued functions. We first obtain bounds for the norm of dyadic Haar shift operators using a Bellman function technique, and then apply the representation theorem to obtain corresponding results for general Calderón-Zygmund operators. We discuss several results for UMD space-valued Calderón-Zygmund operators and show some weighted inequalities for matrix-valued weights. We also prove a version of the matrix-weighted Carleson embedding theorem.

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