Composition Operators with Quasiconformal Symbols

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 $P_{\phi }$ associated with a quasiconformal mapping $\phi$.