Weighted two-parameter Bergman space inequalities

Weighted Two-parameter Bergman Space Inequalities

In this inequality, ∇ denotes the full gradient in R + : ∇ = (∂/∂x1, . . . , ∂/∂xd, ∂/∂y); R + is the usual upper half space Rd×(0,∞); μ is a positive Borel measure defined on R + ; and v is a non-negative function in Lloc(R d). We studied this inequality primarily for p and q in the range 1 < p ≤ q < ∞. For the case in which q ≥ 2, we proved sufficient conditions on μ and v (depending on p, q,...

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

Gleason’s Problem in Weighted Bergman Space on Egg Domains

In the paper, we discuss on the egg domains: Ω a = ξ = (z, w) ∈ C n+m : z ∈ C n , w ∈ C m , |z| 2 + |w| 2/a < 1 , 0 < a ≤ 2. We show that Gleason's problem can be solved in the weight Bergman space on the egg domains. The proof will need the help of the recent work of the second named author on the weighted Bergman projections on this kind of domain. As an application, we obtain a multiplier th...

Composition Operators from the Weighted Bergman Space to the nth Weighted Spaces on the Unit Disc

Weighted Bergman Kernels and Quantization

Let Ω be a bounded pseudoconvex domain in C N , φ, ψ two positive functions on Ω such that − logψ,− log φ are plurisubharmonic, z ∈ Ω a point at which − log φ is smooth and strictly plurisubharmonic, and M a nonnegative integer. We show that as k → ∞, the Bergman kernels with respect to the weights φkψM have an asymptotic expansion KφkψM (x, y) = kN πNφ(x, y)kψ(x, y)M ∞ ∑ j=0 bj(x, y) k −j , b0...