Related papers: Boundedness of the Bergman projection on generaliz…
We give criteria for boundedness of the associated Bergman-type projections on Lp-spaces on Cn with respect to generalized Gaussian weights exp(-|z|^2m). Complete characterization is obtained for 0<m<=1 and 2n/(2n-1)<m<2; partial results…
We apply the Bekoll\'e-Bonami estimate for the (positive) Bergman projection on the weighted $L^p$ spaces on the unit disk. As the consequences, we obtain the boundedness of the Bergman projection on the weighted Sobolev space on the…
We show that weighted Bergman projections corresponding to radially symmetric weights on the unit disc are bounded on Sobolev spaces.
The main purpose of this survey is to gather results on the boundedness of the Bergman projection. First, we shall go over some equivalent norms on weighted Bergman spaces $A^p_\omega$ which are useful in the study of this question. In…
In this article we introduce Variable exponent Fock spaces and study some of their basic properties such as the boundedness of evaluation functionals, density of polynomials, boundedness of a Bergman-type projection and duality.
We bound integral means of the Bergman projection of a function in terms of integral means of the original function. As an application of these results, we bound certain weighted Bergman space norms of derivatives of Bergman projections in…
We study fractional Sobolev and Besov spaces on noncompact Riemannian manifolds with bounded geometry. Usually, these spaces are defined via geodesic normal coordinates which, depending on the problem at hand, may often not be the best…
A class of pseudoconvex domains in $\mathbb{C}^{n}$ generalizing the Hartogs triangle is considered. The $L^p$ boundedness of the Bergman projection associated to these domains is established, for a restricted range of $p$ depending on the…
We obtain some weighted $L^{p}$-Sobolev estimates with gain on $p$ and the weight for solutions of the $\overline{\partial}$-equation in lineally convex domains of finite type in $\mathbb{C}^{n}$ and apply them to obtain weighted…
We investigate $L^p$ regularity of weighted Bergman projections on the unit disc and $L^p$ regularity of ordinary Bergman projections in higher dimensions.
In this paper, we prove the boundedness of the Bergman projection on weighted mixed norm spaces of the upper-half space for some weights that are constructed using the logarithm function and growth functions. Our necessary and sufficient…
In this paper we investigate the regularity properties of weighted Bergman projections for smoothly bounded pseudo-convex domains of finite type in $\mathbb{C}^{n}$. The main result is obtained for weights equal to a non negative rational…
Botelho, Jamison, and Moln\'ar \cite{BJM}, and Geh\' er and \v{S}emrl \cite{GeS} have recently described the general form of surjective isometries of Grassmann spaces of all projections of a fixed finite rank on a Hilbert space $H$. As a…
We prove the boundedness of Bergman type projections in two different analytic function spaces in bounded strongly pseudoconvex domains with the smooth boundary. Our results were previously well-known in the case of the unit disk.
We characterize the boundedness of Hankel bilinear forms on a product of generalized Fock-Sobolev spaces on ${\mathbb C}^n$ with respect to the weight $(1+|z|)^\rho e^{-\frac{\alpha}2|z|^{2\ell}}$, for $\ell\ge 1$, $\alpha>0$ and…
The motivation of this paper is a suggestion by H\"ole of comparing the notions of $\D$-boundedness and boundedness in Probabilistic Normed spaces (briefly PN spaces), with non necessarily continuous triangle functions. Such spaces are here…
The embedding relations between Besov-Triebel-Sobolev spaces and modulation spaces are determined explicitly. We extend the results of Sugimoto[2007]; Wang[2007] and Kobayashi[2011] to the most general cases. And we give the sharp embedding…
In this paper we investigate a two classes of domains in $\mathbb{C}^n$ generalizing the Hartogs triangle. We prove optimal estimates for the mapping properties of the Bergman projection on these domains.
We study the weighted Fock spaces in one and several complex variables. We evaluate the dimension of these spaces in terms of the weight function extending and completing earlier results by Rozenblum-Shirokov and Shigekawa.
We study weighted Besov and Triebel--Lizorkin spaces associated with Hermite expansions and obtain (i) frame decompositions, and (ii) characterizations of continuous Sobolev-type embeddings. The weights we consider generalize the…