Composition Operators with Quasiconformal Symbols

TL;DR

This paper extends the theory of composition operators on analytic Hilbert spaces to include quasiconformal symbols, analyzing boundedness and operator properties, with detailed $L^p$-estimates for related singular integral operators.

Contribution

It introduces the study of composition operators with quasiconformal symbols and provides $L^p$-estimates for associated singular integral operators, expanding the scope beyond analytic symbols.

Findings

Boundedness criteria for composition operators with quasiconformal symbols

$L^p$-estimates for singular integral operators $P_\varphi$

Operator-theoretic properties discussed in the quasiconformal setting

Abstract

This paper seeks to extend the theory of composition operators on analytic functional Hilbert spaces from analytic symbols to quasiconformal ones. The focus is the boundedness but operator-theoretic questions are discussed as well. In particular, we present a thorough analysis of $L^p$-estimates of a class of singular integral operators $P_\varphi$ associated with a quasiconformal mapping $\varphi$.