相关论文: Irregularity of the Bergman projection on worm dom…

Although the Bergman projection operator $\mathbf{B}_{\Omega}$ is defined on $L^2(\Omega)$, its behavior on other $L^p(\Omega)$ spaces for $p\not =2$ is an active research area. We survey some of the recent results on $L^p$ estimates on the…

In this paper we study the regularity of the Szeg\H{o} projection on Lebesgue and Sobolev spaces on the distinguished boundary of the unbounded model worm domain $D_\beta$. We denote by $d_b(D_\beta)$ the distinguished boundary of $D_\beta$…

Let $\Omega$ be a pseudoconvex domain with $C^2$-smooth boundary in $\mathbb CP^n$. We prove that the $\bar\partial-Neumann operator $N$ exists for $(p,q)$-forms on $\Omega$. Furthermore, there exists a $t_0>0$ such that the operators $N$,…

Let $\Omega\subset\dR^d$ be a bounded or an unbounded Lipschitz domain. In this note we address the problem of continuation of functions from the Sobolev space $H^1(\Omega)$ up to functions in the Sobolev space $H^1(\dR^d)$ via a linear…

The Fock-Bargmann-Hartogs domain $D_{n, m}(\mu)$ is defined by $$ D_{n, m}(\mu):=\{(z, w)\in\mathbb{C}^{n}\times\mathbb{C}^m:\Vert w \Vert^2<e^{-\mu\Vert z \Vert^2}\},$$ where $\mu>0.$ The Fock-Bargmann-Hartogs domain $D_{n, m}(\mu)$ is an…

Let $D$ be a bounded strictly pseudoconvex domain in $\mathbb{C}^n$. Assuming $bD \in C^{k+3+\alpha}$ where $k$ is a non-negative integer and $0 < \alpha \leq 1$, we show that 1) the Bergman kernel $B(\cdot, w_0) \in C^{k+ \min\{\alpha,…

Given an n-tuple of multiplication operators on the Bergman space of a bounded pseudoconvex domain in C^n, we study the algebra of their commutants. In particular, we give a geometric description of the maximal C*-subalgebra of this…

We describe along the guidelines of Kohn "Quantitative estimates..." (1999), the constant E_s which is needed to control the commutator of a totally real vector field T with di-bar* in order to have Sobolev s-regularity of the Bergman…

In this note we show that the weighted $L^{2}$-Sobolev estimates obtained by P. Charpentier, Y. Dupain & M. Mounkaila for the weighted Bergman projection of the Hilbert space $L^{2}\left(\Omega,d\mu_{0}\right)$ where $\Omega$ is a smoothly…

Let $\Omega\subset \mathbb{C}^n$ be a smooth bounded pseudoconvex domain and $A^2 (\Omega)$ denote its Bergman space. Let $P:L^2(\Omega)\longrightarrow A^2(\Omega)$ be the Bergman projection. For a measurable $\varphi:\Omega\longrightarrow…

Let $\Omega \subset \mathbb{R}^d$ be bounded open and connected. Suppose that $W^{1,2}(\Omega) \subset L^r(\Omega)$ for some $r > 2$. Let $A$ be a pure second-order elliptic differential operator with bounded real measurable coefficients on…

We study Poincar\'e--Friedrichs--Weber constants for Sobolev differential forms on bounded convex domains and on domains star-shaped with respect to a ball. Generalizing work by Guerini and Savo, our main result shows that the…

We consider generalized Bochner-Riesz operators associated with planar convex domains. We construct domains which yield improved $L^p$ bounds for the Bochner-Riesz over previous results of Seeger-Ziesler and Cladek. The constructions are…

In this article, we study the range of the Cauchy-Riemann operator $\bar\partial$ on domains in the complex projective space $\Bbb{CP}^n$. In particular, we show that $\bar\partial$ does not have closed range in $L^2$ for (2,1)-forms on the…

For $1<p<\infty$ we determine the precise range of $L_p$ Sobolev spaces for which the Haar system is an unconditional basis. We also consider the natural extensions to Triebel-Lizorkin spaces and prove upper and lower bounds for norms of…

In this paper we study the regularity of the Szeg\"o projection on Lebesgue and Sobolev spaces on the boundary of the unbounded model worm domain $D'_\beta$. We consider the Hardy space $H^2(D'_\beta)$. Denoting by $bD'_\beta$ the boundary…

We prove that Heisenberg groups, a.k.a. the boundaries of Siegel domains, minimize the $L^p$ operator norm of the Szeg\H{o} projection in a large class of weighted CR manifolds of hypersurface type.

We study spectral estimates of the divergence form uniform elliptic operators $-\textrm{div}[A(z) \nabla f(z)]$ with the Dirichlet boundary condition in bounded non-Lipschitz simply connected domains $\Omega \subset \mathbb C$. The…

We generalise results by Lamberti and Lanza de Cristoforis (2005) concerning the continuity of projections onto eigenspaces of self-adjoint differential operators with compact inverses as the (spatial) domain of the functions is perturbed…

We study $L^p$ bounds on spectral projections for the Laplace operator on compact Riemannian manifolds, restricted to small frequency dependent neighborhoods of submanifolds. In particular, if $\lambda$ is a frequency and the size of the…