Related papers: A generalized Hilbert matrix acting on Hardy space…

Let $(\mathcal{X},d,\mu)$ be a metric measure space satisfying the so-called upper doubling condition and the geometrically doubling condition. Let $T$ be a Calder\'{o}n-Zygmund operator with kernel satisfying only the size condition and…

The Fock-Bargmann-Hartogs domain $D_{n,m}(\mu)$ ($\mu>0$) in $\mathbb{C}^{n+m}$ is defined by the inequality $\|w\|^2<e^{-\mu\|z\|^2},$ where $(z,w)\in \mathbb{C}^n\times \mathbb{C}^m$, which is an unbounded non-hyperbolic domain in…

Let $n$ be a positive integer and $\mathbf{g}=(g_0,g_1,\cdots,g_{n-1})$, with $g_k\in H(\mathbb{D})$ for $k=0,1,\cdots,n-1$. Let $I_{\mathbf{g}}^{(n)}$ be the generalized Volterra-type operators on $H(\mathbb{C})$, which is represented as…

We consider the generalised Krein-Feller operator $\Delta_{\nu, \mu} $ with respect to compactly supported Borel probability measures $\mu$ and $\nu$ with the natural restrictions that $\mu$ is atomless, the supp$(\nu)\subseteq$supp$(\mu)$…

Given a strictly increasing sequence $\Lambda=(\lambda_n)$ of nonegative real numbers, with $\sum_{n=1}^\infty \frac{1}{\lambda_n}<\infty$, the M\"untz spaces $M_\Lambda^p$ are defined as the closure in $L^p([0,1])$ of the monomials…

We deal with a reverse Carleson measure inequality for the tent spaces of analytic functions in the unit disc $\mathbb{D}$ of the complex plane. The tent spaces of measurable functions were introduced by Coifman, Meyer and Stein. Let $1\leq…

Let $(X,\mu)$ be a space with a finite measure $\mu$, let $A$ and $B$ be $w^*$-closed subalgebras of $L^{\infty}(\mu)$, and let $C$ and $D$ be closed subspaces of $L^p(\mu)$ ($1<p<\infty$) that are modules over $A$ and $B$, respectively.…

Consider a bounded symmetric domain $\Omega$ with a finite pseudo-reflection group acting on it as a subgroup of the group of automorphisms. This gives rise to quotient domains by means of basic polynomials $\theta$ which by virtue of being…

We compute the exact value of the essential norm of a generalized Hilbert matrix operator acting on weighted Bergman spaces $A^p_v$ and weighted Banach spaces $H^\infty_v$ of analytic functions, where $v$ is a general radial weight. In…

We give a sufficient and necessary condition for an analytic function $f(z)$ on the unit ball $\BB$ in $\CC^n$ with Hadamard gaps, that is, for $f(z)=\sum_{k=1}^\infty P_{n_k}(z)$ where $P_{n_k}(z)$ is a homogeneous polynomial of degree…

A multiplicative Hankel operator is an operator with matrix representation $M(\alpha) = \{\alpha(nm)\}_{n,m=1}^\infty$, where $\alpha$ is the generating sequence of $M(\alpha)$. Let $\mathcal{M}$ and $\mathcal{M}_0$ denote the spaces of…

In this paper we initiate the study of absolute summability for big and little Hankel operators $ H_f^\beta,h_f^\beta:A_\alpha^p(\mathbb{B}_n)\to L^q(\mathbb{B}_n,dv_\beta), $ acting between weighted Bergman and weighted Lebesgue spaces on…

A Borel probability measure $\mu$ on a locally compact group is called a spectral measure if there exists a subset of continuous group characters which forms an orthogonal basis of the Hilbert space $L^2(\mu)$. In this paper, we…

For $1\le p<\infty$, let $F^p_\varphi$ be the Fock spaces on ${\mathbb C}^n$ with the weight function $\varphi$ that \(\varphi \in {\mathcal{C}}^{2}\left( {\mathbb{C}}^{n}\right)\) is real-valued and satisfies $ m{\omega }_{0} \leq…

For a compact subset $K\subset \mathbb C$ and a positive finite Borel measure $\mu$ supported on $K,$ let $\text{Rat}(K)$ denote the space of rational functions with poles off $K,$ let $R^\infty (K,\mu)$ be the weak-star closure of…

In this paper, we give a universal description of the boundedness and compactness of Toeplitz operator $\mathcal{T}_\mu^\omega$ between Bergman spaces $A_\eta^p$ and $A_\upsilon^q$ when $\mu$ is a positive Borel measure, $1<p,q<\infty$ and…

For a locally compact quantum group $\G$ with tracial Haar weight $\varphi$, and a quantum measure $\mu$ on $\G$, we study the space ${H}_\mu^p$ of $\mu$-harmonic operators in the non-commutative $L^p$-space ${L}^p(\G)$ associated to the…

A certain class of matrix-valued Borel matrix functions is introduced and it is shown that all functions of that class naturally operate on any operator T in a finite type I von Neumann algebra M in a way such that uniformly bounded…

In the setting of tube domains over symmetric cones, $T_\Omega$, we study the characterization of the positive Borel measures $\mu$ for which the Hardy space $H^p$ is continuously embedded into the Lebesgue space $L^q (T_\Omega, d\mu)$,…

The paper considers the Hilbert space $\hat{H}_r$ of real functions summable with the square $L^2(a,b)_r$ on any interval $\{(a,b)_r\}_{r=1}^{\infty}\in \mathbb{R}$. It is shown on the basis of the theorem on zeros of real orthogonal…