Brennan's conjecture for composition operators on Sobolev spaces

Abstract

We show that Brennan's conjecture is equivalent to boundedness of composition operators on homogeneous Sobolev spaces generated by conformal homeomorphisms of simply connected plane domains to the unit disc.

8 pages

Cited by in corpus (7)

• On the First Eigenvalues of Free Vibrating Membrane in Conformal Regular Domains
• Conformal spectral stability for the Dirichlet-Laplace operator
• Spectral Estimates of the $p$-Laplace Neumann operator and Brennan's Conjecture
• Universal conformal weights on Sobolev spaces
• Conformal Spectral Stability Estimates for the Neumann Laplacian
• Spectral Properties of the Neumann-Laplace operator in Quasiconformal Regular Domains
• Sobolev homeomorphisms and Brennan's conjecture