The Bergman projection in spaces of entire functions

Abstract

We establish L p -estimates for the weighted Bergman projection on a nonsingular cone. We apply these results to the weighted Fock space with respect to the minimal norm in C n .

Bergman kernels, TYZ expansions and Hankel operators on the Kepler manifold

“…We leave the details to the interested reader. For m = 1, (20) recovers the formula from Gonessa and Youssfi [12].…”

“…Here R φ is the square root of the radius of convergence of the series (11). We let L 2 φ (C n ) denote the space of all measurable functions f in C n verifying (12). Finally, we define the operators ∆ j , j = 0, 1, acting on power series in z by their actions on the monomials z m as follows…”

A duality theorem for certain fock spaces

“…If N is any complex norm in C n such that N 2 (x) = x 2 = n j=1 x 2 j for x ∈ R n and N (z) = z for z ∈ C n , then N * (z)/ √ 2 ≤ N (z) for z ∈ C n . Moreover, this norm was shown to be of interest in the study of several problems related to proper holomorphic mappings and the Bergman kernel, see [7,8,13,14,15] for example. For any s > 0 and 0 < p ≤ ∞ we let L p s denote the space of Lebesgue mesurable functions f on C n such that f e −φ ∈ L p (C n , ρ −2 dA).…”

$l^p-l^q$ estimates of Bergman projector on the minimal ball

“…More precisely, if N is any complex norm in C n such that N (x) = |x| = n j=1 x 2 j for x ∈ R n and N (z) ≤ |z| for z ∈ C n , then N * (z)/ √ 2 ≤ N (z) for z ∈ C n . Moreover, this norm was shown to be of interest in the study of several problems related to proper holomorphic mappings and the Bergman kernel, see for example [2,3,5,6]. The domain B * is the first bounded domain in C n which is neither Reinhardt nor homogeneous, and for which we have an explicit formula for its Bergman kernel.…”