NOTES ON BERGMAN PROJECTION TYPE OPERATOR RELATED WITH BESOV SPACE

Composition Operator on Bergman-Orlicz Space

Recommended by Shusen Ding Let D denote the open unit disk in the complex plane and let dAz denote the normalized area measure on D. Φ α is defined as follows L Φ α {f ∈ HD : D ΦΦlog |fz|1 − |z| 2 α dAz < ∞}. Let ϕ be an analytic self-map of D. The composition operator C ϕ induced by ϕ is defined by C ϕ f f • ϕ for f analytic in D. We prove that the composition operator C ϕ is compact on L Φ α ...

On a New Integral-Type Operator from the Weighted Bergman Space to the Bloch-Type Space on the Unit Ball

We introduce an integral-type operator, denoted by P φ , on the space of holomorphic functions on the unit ball B ⊂ C, which is an extension of the product of composition and integral operators on the unit disk. The operator norm of P φ from the weighted Bergman space A p α B to the Bloch-type space Bμ B or the little Bloch-type space Bμ,0 B is calculated. The compactness of the operator is cha...

Compact Composition Operator on Weighted Bergman-Orlicz Space

In this paper we study the weighted Bergman-Orlicz spaces Aα. Among other properties we get that Aα is a Banach space with the Luxemburg norm. We show that the set of analytic polynomials is dense in Aα. We also study compactness and continuity of the composition operator on Aα. Mathematics Subject Classification: 46E30, 47B33

OPERATOR THEORY ON HILBERT SPACE Class notes

Analytic Besov spaces and Hardy-type inequalities in tube domains over symmetric cones

We give various equivalent formulations to the (partially) open problem about Lboundedness of Bergman projections in tubes over cones. Namely, we show that such boundedness is equivalent to the duality identity between Bergman spaces, A ′ = (Ap)∗, and also to a Hardy type inequality related to the wave operator. We introduce analytic Besov spaces in tubes over cones, for which such Hardy inequa...