Composition Operators Between Hardy Spaces on Linearly Convex Domains in $$\mathbb {C}^2$$ C 2

Abstract

We study composition operators acting between Hardy spaces $$H^p(\Omega )$$ , where $$\Omega \subset \mathbb {C}^2$$ is a smoothly bounded, $$\mathbb {C}$$ -linearly convex domain admitting the so-called F-type at all boundary points. This F-type domains contain certain convex domains of finite type and many cases of infinite type in the sense of Range. Criteria for boundedness and compactness of such composition operators are established. Our approach is based on the Cauchy–Leray kernel.