Optimal norm estimate of operators related to the harmonic Bergman projection on the ball

A Sharp Norm Estimate of the Bergman Projection on L Spaces

We show that the norm of the Bergman projection on L of the unit ball in C is comparable to csc(π/p) for 1 < p <∞.

Compact Composition Operators on Bergman Spaces of the Unit Ball

Under a mild condition we show that a composition operator Cφ is compact on the Bergman space Aα of the open unit ball in C if and only if (1− |z|)/(1− |φ(z)|) → 0 as |z| → 1−.

Boundedness of the Bergman Type Operators on Mixed Norm Spaces

Conditions sufficient for boundedness of the Bergman type operators on certain mixed norm spaces Lp,q(φ) (0 < p < 1, 1 < q <∞) of functions on the unit ball of Cn are given, and this is used to solve Gleason’s problem for the mixed norm spaces Hp,q(φ) (0 < p < 1, 1 < q <∞).

On Some Class of Integral Operators Related to the Bergman Projection

The Essential Norm of the Generalized Hankel Operators on the Bergman Space of the Unit Ball in Cn

and Applied Analysis 3 to define a kind of generalized Hankel operator: