Related papers: Function Spaces Related to the Dirichlet Space

Let $\mathscr T=(V, \mathcal E)$ be a leafless, locally finite rooted directed tree. We associate with $\mathscr T$ a one parameter family of Dirichlet spaces $\mathscr H_q~(q \geqslant 1)$, which turn out to be Hilbert spaces of…

We introduce a new class of Hardy spaces $H^{\varphi(\cdot,\cdot)}(\mathbb R^n)$, called Hardy spaces of Musielak-Orlicz type, which generalize the Hardy-Orlicz spaces of Janson and the weighted Hardy spaces of Garc\'ia-Cuerva, Str\"omberg,…

We introduce two kinds of quasi-inner functions. Since every rationally invariant subspace for a shift operator $S_K$ on a vector-valued Hardy space $H^{2}(\Omega,K)$ is generated by a quasi-inner function, we also provide relationships of…

We realize the relative discrete series of a weighted $L^2$-space on a bounded symmetric doamin as kernels of invariant Cauchy-Riemann operator, and thus as the spaces of nearly holomorphic functions.

Recently, in arXiv:2304.07149, a bridge was made between the very active area of spaces of Lipschitz real functions on a metric space and holomorphic functions on an open subset of a Banach space. This was done by introducing and studying…

We discuss the notion of an inner function for spaces of analytic functions in multiply connected domains in $\mathbb{C}$, giving a historical overview and comparing several possible definitions. We explore connections between inner…

Matrix valued inner functions on the bidisk have a number of natural subspaces of the Hardy space on the torus associated to them. We study their relationship to Agler decompositions, regularity up to the boundary, and restriction maps into…

In this paper, we introduce a general class of weighted spaces of holomorphic Dirichlet series (with real frequencies) analytic in some half-plane and study composition operators on these spaces. In the particular case when the symbol…

The objective of this paper is to characterize harmonic Hardy spaces and a boundary behavior of harmonic functions on a smooth domain in real Euclidean space.

In this paper, we establish several different characterizations of the vanishing mean oscillation space associated with Neumann Laplacian $\Delta_N$, written ${\rm VMO}_{\Delta_N}(\mathbb{R}^n)$. We first describe it with the classical…

We give an extension to certain \textit{RD-space} $\X$, i.e space of homogeneous type in the sense of Coifman and Weiss, which has the reverse doubling property, of the definition and various properties of the product of functions in…

In this work, we construct examples of holomorphic functions in $D_2(\B_2)$, the Dirichlet space on $\B_2$, for which there exists an index $\alpha_c \in [\frac12,2]$ such that the function is cyclic in $D_\alpha(\B_2)$ if and only if…

We consider the $(1,2)$-Sobolev space $W^{1,2}(U)$ on subsets $U$ in an abstract Wiener space, which is regarded as a canonical Dirichlet space on $U$. We prove that $W^{1,2}(U)$ has smooth cylindrical functions as a dense subset if $U$ is…

In this paper we investigate the reproducing kernel Hilbert space where the polylogarithm appears as kernel functions. This investigation begins with the properties of functions in this space, and here a connection to the classical Hardy…

We describe the strong dual space $({\mathcal O}^s (D))^*$ for the space ${\mathcal O}^s (D) = H^s (D) \cap {\mathcal O} (D)$ of holomorphic functions from the Sobolev space $H^s(D)$, $s \in \mathbb Z$, over a bounded simply connected plane…

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…

Let $\Delta$ and $L=\Delta -\|\mathbf x\|^2$ be the Dunkl Laplacian and the Dunkl harmonic oscillator respectively. We define the Hardy space $\mathcal H^1$ associated with the Dunkl harmonic oscillator by means of the nontangential maximal…

We study composition operators on spaces of double Dirichlet series, focusing our interest on the characterization of the composition operators of the space of bounded double Dirichlet series $\HCdos$. We also show how the composition…

We prove some isoperimetric type inequalities for real harmonic functions in the unit disk belonging to the Hardy space $h^p$, $p>1$ and for complex harmonic functions in $h^4$. The results extend some recent results on the area. Further we…

Let $L$ be a one-to-one operator of type $\omega$ in $L^2(\mathbb{R}^n)$, with $\omega\in[0,\,\pi/2)$, which has a bounded holomorphic functional calculus and satisfies the Davies-Gaffney estimates. Let $p(\cdot):\ \mathbb{R}^n\to(0,\,1]$…