Related papers: A local Douglas formula for higher order weighted …

It is believed that Dirichlet series with a functional equation and Euler product of a particular form are associated to holomorphic newforms on a Hecke congruence group. We perform computer algebra experiments which find that in certain…

In this paper, we shall consider the killing transform induced by a multiplicative functional on regular Dirichlet subspaces of a fixed Dirichlet form. Roughly speaking, a regular Dirichlet subspace is a closed subspace with Dirichlet and…

We initiate a systematic study of the cohomology of cluster varieties. We introduce the Louise property for cluster algebras that holds for all acyclic cluster algebras, and for most cluster algebras arising from marked surfaces. For…

We study a class of non-divergence form elliptic and parabolic equations with singular first-order coefficients in an upper half space with the homogeneous Dirichlet boundary condition. In the simplest setting, the operators in the…

Let $\ce$ be a Dirichlet form on $L_2(X\,;\mu)$ where $(X,\mu)$ is locally compact $\sigma$-compact measure space. Assume $\ce$ is inner regular, i.e.\ regular in restriction to functions of compact support, and local in the sense that…

Harmonically weighted Dirichlet spaces $\mathcal{D}_\mu$ and de Branges_Rovnyak spaces $\mathcal{H}(b)$ are two fundamental structures in analytic function theory exhibiting rich and often complementary properties. The question of when…

We describe the closures of locally divergent orbitsunder the action of tori on Hilbert modular spaces of rank r = 2. In particular, we prove that if D is a maximal R-split torus acting on a real Hilbert modular space then every locally…

We establish an analogue of Wolff's theorem on ideals in $H^{\infty}(\mathbb{D})$ for the multiplier algebra of weighted Dirichlet space.

We investigate a relation between the Mordell-Tornheim type of multiple Dirichlet series and a confluent hypergeometric function. We prove it by applying the Mellin-Barnes integral formula. Also, main results in this paper contain two kinds…

We prove well-posedness and higher-order regularity for a linear structurally damped plate equation with inhomogeneous Dirichlet--Neumann boundary conditions on the half-space and on bounded domains. To this end, we study maximal regularity…

We discuss a notion, originally introduced by Aleman in one variable, of Dirichlet-type space $\mathcal D(\mu_1,\mu_2)$ on the unit bidisc $\mathbb D^2,$ with superharmonic weights related to finite positive Borel measures $\mu_1,\mu_2$ on…

This work is devoted to the comparison of de Branges--Rovnyak $H(b)$ spaces harmonically weighted Dirichlet spaces $\mathcal{D}_\mu$. We completely characterize which $H(b)$ spaces are also harmonically weighted Dirichlet spaces…

In this article we examine Dirichlet type spaces in the unit polydisc, and multipliers between these spaces. These results extend the corresponding work of G. D. Taylor in the unit disc. In addition, we consider functions on the polydisc…

Using Carleson measure theorem of weighted Bergman spaces, we provide a complete characterization of embedding theorem for Dirichlet type spaces. As an application, we study the Volterra integral operator and multipliers for Dirichlet type…

In this paper we establish the characterization of the weighted BMO via two weight commutators in the settings of the Neumann Laplacian $\Delta_{N_+}$ on the upper half space $\mathbb{R}^n_+$ and the reflection Neumann Laplacian $\Delta_N$…

We show that if $u$ is a solution to a linear elliptic differential equation of order $2m\geq 2$ in the half-space with $t$-independent coefficients, and if $u$ satisfies certain area integral estimates, then the Dirichlet and Neumann…

Kubota's integral formula expresses the intrinsic volumes of a convex body as averages over its projections onto linear subspaces. In this work, we introduce a new class of Kubota-type formulas for mixed area measures adapted to rotations…

In this note some structural properties of grand variable exponent Lebesgue/ Morrey spaces over spaces of homogeneous type are obtained. In particular, it is proved that the closure of the class of bounded functions and the closure of…

In this note, we present explicit conditions for symmetric gradient type Dirichlet forms to be recurrent. This type of Dirichlet form is typically strongly local and hence associated to a diffusion. We consider the one dimensional case and…

We analyze the singularities of rational inner functions on the unit bidisk and study both when these functions belong to Dirichlet-type spaces and when their partial derivatives belong to Hardy spaces. We characterize derivative…