Pointwise estimates for the Bergman kernel of the weighted Fock space

Abstract

We prove upper pointwise estimates for the Bergman kernel of the weighted Fock space of entire functions in $L^2(e^{-2\varphi })$ where $\varphi$ is a subharmonic function with $\Delta \varphi$ a doubling measure. We derive estimates for the canonical solution operator to the inhomogeneous Cauchy-Riemann equation and we characterize the compactness of this operator in terms of $\Delta \varphi$.

Cited by in corpus (14)

• Some spectral properties of the canonical solution operator to $\bar{\partial }$ on weighted Fock spaces
• On the weighted $\bar{\partial }$-Neumann problem on unbounded domains
• Fredholm Toeplitz operators on doubling Fock spaces
• Boundedness of the Bergman projection on $L^p$ spaces with exponential weights
• Reproducing kernel estimates, bounded projections and duality on large weighted Bergman spaces
• Inhomogenous random zero sets
• Small Hankel operators on generalized Fock spaces
• Exponential decay of Bergman kernels on complete Hermitian manifolds with Ricci curvature bounded from below
• Microscopic densities and Fock-Sobolev spaces
• On some spectral properties of the weighted $\overline{\partial }$-Neumann problem
• On the weighted $L^2$ estimate for the $k$-Cauchy-Fueter operator and the weighted $k$-Bergman kernel
• Discreteness of spectrum for the $\overline{\partial }$-Neumann Laplacian on manifolds of bounded geometry
• On the Bergman kernel in weighted monogenic Bargmann-Fock spaces
• Hankel Bilinear forms on generalized Fock-Sobolev spaces on ${\mathbb{C}}^n$