COMPACT COMPOSITION OPERATORS ON WEIGHTED BERGMAN SPACES ON BOUNDED SYMMETRIC DOMAINS

【摘要】 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 Cφ is compact on L q a (Ω, dv β ) if and only if K ( φ ( z ) ,φ ( z )) K ( z,z ) → 0 as z →φΩ under a mild condition, where K(z, w) is the Bergman kernel.更多还原

【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 Cφ is compact on L q a (Ω, dv β ) if and only if K ( φ ( z ) ,φ ( z )) K ( z,z ) → 0 as z → φΩ under a mild condition, where K(z, w) is the Bergman kernel.更多还原