Compact composition operators on weighted Bergman spaces on bounded symmetric domains

Abstract

In this article, we borrow the idea of using Schur's test to characterize the compactness of composition operators on the weighted Bergman spaces in a bounded symmetric domain Ω, and verify that C ϕ is compact on L q a(Ω, d vβ) if and only if K ( φ ( z ) , φ ( z ) ) K ( z , z ) → 0 as z → ∂Ω under a mild condition, where K(z, w) is the Bergman kernel.