Related papers: Weighted Bergman Projections on the Hartogs Triang…
Let $w$ be a Muckenhoupt $A_2(\mathbb{R}^n)$ weight and $L_w:=-w^{-1}\mathop\mathrm{div}(A\nabla)$ the degenerate elliptic operator on the Euclidean space $\mathbb{R}^n$. In this article, the authors establish the Riesz transform…
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 describe the range of of weighted Cauchy transform and its $k$-Bergman projection when action on weighted true poly-Bargmann spaces constituting an orthogonal Hilbertian decomposition of the Hilbert space of Gaussian functions on the…
In this paper we investigate a class of domains $\Omega^{n+1}_k =\{(z,w)\in \mathbb{C}^n\times \mathbb{C}: |z|^k < |w| < 1\}$ for $k \in \mathbb{Z}^+$ which generalizes the Hartogs triangle. we first obtain the new explicit formulas for the…
We study a degenerate elliptic system with variable exponents. Using the variational approach and some recent theory on weighted Lebesgue and Sobolev spaces with variable exponents, we prove the existence of at least two distinct nontrivial…
We prove two sharp estimates for the subspace of a standard weighted Bergman space that consists of functions vanishing at a given point (with prescribed multiplicity).
We obtain large time decay estimates on weighted $L^p$ spaces for solutions to the wave equation with real-valued potential $V(x)=O(|x|^{-2-a})$, $a>0$, for $|x|>1$.
The definition of classical holomorphic function spaces such as the Hardy space or the Dirichlet space on the Hartogs triangle is not canonical. In this paper we introduce a natural family of holomorphic function spaces on the Hartogs…
In this note we extend the concept height on projective spaces to that of weighted height on weighted projective spaces and show how such a height can be computed. We prove some of the basic properties of the weighted height and show how it…
We establish up to the boundary regularity estimates in weighted $L^{p}$ spaces with Muckenhoupt weights $A_{p}$ for weak solutions to the Hodge systems \begin{align*} d^{\ast}\left(Ad\omega\right) +…
Regularity and irregularity of the Bergman projection on $L^p$ spaces is established on a natural family of bounded, pseudoconvex domains. The family is parameterized by a real variable $\gamma$. A surprising consequence of the analysis is…
\begin{abstract} We obtain sharp $L^p\rightarrow L^q$ hypercontractive inequalities for the weighted Bergman spaces on the unit disk $\mathbb{D}$ with the usual weights \\ $\frac{\alpha-1}{\pi}(1-|z|^2)^{\alpha-2},\alpha>1$ for $q\geq 2,$…
We prove that a conformal mapping defined on the unit disk belongs to a weighted Bergman space if and only if certain integrals involving the harmonic measure converge. With the aid of this theorem, we give a geometric characterization of…
This paper proves $L^p$ decay estimates for Schr\"{o}dinger's and wave equations with scalar potentials on three-dimensional Riemannian manifolds. The main result regards small perturbations of a metric with constant negative sectional…
In this paper, we introduce degenertae generalized hypergeometric functions and study degenerate hypergeometric numbers of order p. These numbers involving of lambda-binomial coefficients and lambda-falling sequence, and can be represented…
We use convex integration techniques to provide examples of failure of weighted Calder\'{o}n-Zygmund estimates for degenerate linear elliptic PDEs when the weights are in $A_p$, $p > 2$.
We investigate the quadratic descent of totally decomposable algebras with involution of orthogonal type in characteristic two. Both separable and inseparable extensions are included.
We establish Strichartz estimates (both reversed and some direct ones), pointwise decay estimates, and weighted decay estimates for the linear wave equation in dimension two with an almost scaling-critical potential, in the case when there…
We establish weighted weak-type bounds for the Bergman projection with respect to Bekoll\'e-Bonami characteristics. We present two proofs of an improved quantitative weak-type $(1,1)$ estimate, as well as sharp weak-type $(p,p)$ bounds for…
Expected duality and approximation properties are shown to fail on Bergman spaces of domains in $\mathbb{C}^n$, via examples. When the domain admits an operator satisfying certain mapping properties, positive duality and approximation…