Related papers: Zero sequences, factorization and sampling measure…

In this paper, some characterizations for the compact difference of composition operators on Bergman spaces $A^p_\omega$ with doubling weight are given, which extend Moorhouse's characterization for the difference of composition operators…

Compact differences of two weighted composition operators acting from the weighted Bergman space $A^p_\omega$ to another weighted Bergman space $A^q_\nu$, where $0<p\le q<\infty$ and $\omega,\nu$ belong to the class $\mathcal{D}$ of radial…

The two weights inequality for Hankel operators $$\|H_f^\omega (\cdot)\|_{L_\eta^q}\leq C \|\cdot\|_{A_v^p},$$ induced by some radial weights under the regular assumptions is considered, the boundedness and compactness of Hankel operators…

For $0<p<\infty$, $\Psi:[0,\infty)\to(0,\infty)$ and a finite positive Borel measure $\mu$ on the unit disc $\mathbb{D}$, the Lebesgue--Zygmund space $L^p_{\mu,\Psi}$ consists of all measurable functions $f$ such that $\lVert f…

Suppose that $\omega$ is a radial weight on the unit disk that satisfies both forward and reverse doubling conditions. Using Carleson measures and $T1$-type conditions, we obtain necessary and sufficient conditions of the positive Borel…

In this paper, we focus on the weighted Bergman spaces $A_{\varphi}^{p}$ in $\mathbb{D}$ with $\varphi\in\mathcal{W}_{0}$. We first give characterizations of those finite positive Borel measures $\mu$ in $\mathbb{D}$ such that the embedding…

In this paper, we investigate the boundedness, compactness, essential norm and the Schatten class of weighted composition operators $uC_\varphi$ on Bergman type spaces $A_\omega^p $ with double weight $\omega$. Let $X=\{u\in H(D):…

In this paper, we characterize invertible Toeplitz products on a number of Banach spaces of analytic functions, including weighted Bergman space $L^p_a (\mathbb{B}_n, dv_\gamma)$, the Hardy space $H^p(\partial \mathbb{D})$, and the weighted…

For $0<p,q<\infty$ and $\omega$ a radial weight, the space $L^{p,q}_\omega$ consists of complex-valued measurable functions $f$ on the unit disk such that $$ \| f\|_{L^{p,q}_\omega}^q = \int_0^1 \left…

The usual examples of Bergman spaces consist of the closure of an algebra of holomorphic functions on a domain. One can also take the real part of such functions, but essentially one is looking at the same object. In this paper the author…

The motivation of this paper comes from the two weight inequality $$\|P_\omega(f)\|_{L^p_v}\le C\|f\|_{L^p_v},\quad f\in L^p_v,$$ for the Bergman projection $P_\omega$ in the unit disc. We show that the boundedness of $P_\omega$ on $L^p_v$…

For a real number $\alpha$ the Hilbert spaces $\mathscr{D}_\alpha$ consists of those Dirichlet series $\sum_{n=1}^\infty a_n/n^s$ for which $\sum_{n=1}^\infty |a_n|^2/[d(n)]^\alpha < \infty$, where $d(n)$ denotes the number of divisors of…

Using Khinchin's inequality, Ger$\check{\mbox{s}}$gorin's theorem and the atomic decomposition of Bergman spaces, we estimate the norm and essential norm of Stevi\'c-Sharma type operators from weighted Bergman spaces $A_\omega^p$ to…

The purpose of the paper is to study the operators on the weighted Bergman spaces on the unit disk ${\mathbb{D}}$, denoted by $A^{p}_{\lambda,w}({\mathbb{D}})$, that are associated with a class of generalized analytic functions, named the…

Let $X$ be a metric space equipped with a metric $d$ and a nonnegative Borel measure $\mu$ satisfying the doubling property and let $\{\mathcal{A}_t\}_{t>0}$, be a generalized approximations to the identity, for example $\{\mathcal{A}_t\}$…

The author showed that a sequence in the unit disk is a zero sequence for the Bergman space $A^p$ if and only if a certain weighted space $L^p(W}$ contains a nontrivial analytic function. In this paper it is shown that the sequence is an…

The purpose of this paper is to establish an atomic decomposition for functions in the weighted mixed norm space $A^{p,q}_\omega$ induced by a radial weight $\omega$ in the unit disc admitting a two-sided doubling condition. The obtained…

Let $\omega$ and $\nu$ be radial weights on the unit disc of the complex plane, and denote $\sigma=\omega^{p'}\nu^{-\frac{p'}p}$ and $\omega_x =\int_0^1 s^x \omega(s)\,ds$ for all $1\le x<\infty$. Consider the one-weight inequality…

For $\lambda\ge0$, a $C^2$ function $f$ defined on the unit disk ${{\mathbb D}}$ is said to be $\lambda$-analytic if $D_{\bar{z}}f=0$, where $D_{\bar{z}}$ is the (complex) Dunkl operator given by…

We prove that if a weight is a Bekoll\'{e}-Bonami weight for some $q$ and it satisfies another simple condition that depends on $0 < p < \infty$, then the operator taking a function to its harmonic conjugate is bounded on the harmonic…