Related papers: Bergman projection induced by radial weight

For $0<p<\infty$, we give a complete description of nonnegative radial weight functions $\omega$ on the open unit disk $\mathbb{D}$ such that $$ \int_{\mathbb{D}} |f'(z)|^p (1-|z|^2)^{p-2}\omega(z)dA(z)<\infty $$ if and only if $$…

We explore the connection between $p$-regular operators on Banach function spaces and weighted $p$-estimates. In particular, our results focus on the following problem. Given finite measure spaces $\mu$ and $\nu$, let $T$ be an operator…

We use induction and interpolation techniques to prove that a composition operator induced by a map $\phi$ is bounded on the weighted Bergman space $\A^2_\alpha(\mathbb{H})$ of the right half-plane if and only if $\phi$ fixes $\infty$…

Let $\alpha\in (0, 1]$, $\beta\in [0, n)$ and $T_{\Omega,\beta}$ be a singular or fractional integral operator with homogeneous kernel $\Omega$. In this article, a CMO type space ${\rm CMO}_\alpha(\mathbb R^n)$ is introduced and studied. In…

We prove the boundedness of Bergman type projections in two different analytic function spaces in bounded strongly pseudoconvex domains with the smooth boundary. Our results were previously well-known in the case of the unit disk.

If a bounded domain can be covered by the polydisk through a rational proper holomorphic map, then the Bergman projection is $L^p$-bounded for $p$ in a certain range depending on the ramified rational covering. This result can be applied to…

In this article we address the question of characterizing the sequences of complex numbers $(\eta )=\{ \eta_n\}_{n=0}^\infty $ whose associated Rhaly operator $\mathcal R_{(\eta )}$ is bounded or compact on the Hardy spaces $H^p$ ($1\le…

The so-called weighted solid Cauchy transform, from inside the unit disc into the complement of its closure, is considered and their basic properties such as boundedness is studied for appropriate probability measures. The action the disc…

In this paper a weighted variable exponent Lebesgue spaces $L_{p(x), \omega}$ for $0< p(x)< 1$ is investigated. We show that this spaces is a quasi-Banach spaces. Note that embedding theorem between weight variable Lebesgue spaces is…

We study the boundedness of composition operators on the weighted Bergman spaces and the Hardy space over the polydisc. For arbitrary polydisc we prove the rank sufficiency theorem which, in particular, provides us with a simple criterion…

In this paper, inspired by the work of Da Lio-Rivi\`{e}re-Wettstein, we investigate the boundary-value characterizations of weighted Bergman spaces and establish a weighted Da Lio-Rivi\`{e}re-Wettstein inequality. In addition, we obtain…

A variety of norm inequalities related to Bergman and Dirichlet spaces induced by radial weights are considered. Some of the results obtained can be considered as generalizations of certain known special cases while most of the estimates…

Let $A_{\alpha}^{p}(\mathbb{B}^n;\mathbb{C}^d)$ be the weighted Bergman space on the unit ball $\mathbb{B}^n$ of $\mathbb{C}^n$ of functions taking values in $\mathbb{C}^d$. For $1<p<\infty$ let $\mathcal{T}_{p,\alpha}$ be the algebra…

In this paper, we obtain a complete characterization for the compact difference of two composition operators acting on Bergman spaces with a rapidly decreasing weight $\omega=e^{-\eta}$, $\Delta\eta>0$. In addition, we provide simple…

Boundary Behaviour of Weighted Bergman Kernels: For a planar domain $D \subset \mathbb{C}$ and an admissible weight function $\mu$ on it, some aspects of the boundary behaviour of the corresponding weighted Bergman kernel $K_{D, \mu}$ are…

It is known that the Bergman projection operator maps the space of essentially bounded functions in the unit ball in the d-dimensional complex vector space onto the Bloch space of the unit ball. This paper deals with the various semi-norms…

We characterize the weights for which we have the boundedness of standard weighted integral operators induced by the Bergman-Besov kernels acting between two general weighted Lebesgue classes on the unit ball of $\mathbb{C}^N$ in terms of…

Let $\mathbb{B}^d$ be the unit ball on the complex space $\mathbb{C}^d$ with normalized Lebesgue measure $dv.$ For $\alpha\in\mathbb{R},$ denote $k_\alpha(z,w)=\frac{1}{(1-\langle z,w\rangle)^\alpha},$ the Bergman-type integral operator…

In a celebrated conjecture D.Sarason stated a necessary and sufficient condition on the symbols f, g in the Bergman space, L^2_a(\Delta) of the unit disk, \Delta, for the products T_{f}T_{\bar g} of associated Toeplitz operators to be…

For the weight function $\prod_{i=1}^{d+1}|x_i|^{2\k_i}$ on the unit sphere, sharp local estimates of the orthogonal projection operators are obtained and used to prove the convergence of the Ces\`aro $(C,\delta)$ means in the weighted…