Related papers: Two weight inequality for Bergman projection

The boundedness of the small Hankel operator $h_f^\nu(g)=P_\nu(f\bar{g})$, induced by an analytic symbol $f$ and the Bergman projection $P_\nu$ associated to $\nu$, acting from the weighted Bergman space $A^p_\om$ to $A^q_\nu$ is…

This monograph is devoted to the study of the weighted Bergman space $A^p_\om$ of the unit disc $\D$ that is induced by a radial continuous weight $\om$ satisfying {equation}\label{absteq} \lim_{r\to…

Let $v(r)=\exp\left(-\frac{\alpha}{1-r}\right)$ with $\alpha>0$, and let $\mathbb{D}$ be the unit disc in the complex plane. Denote by $A^p_v$ the subspace of analytic functions of $L^p(\mathbb{D},v)$ and let $P_v$ be the orthogonal…

Let $0<p<\infty$ and $\Psi: [0,1) \to (0,\infty)$, and let $\mu$ be a finite positive Borel measure on the unit disc $\mathbb{D}$ of the complex plane. We define the Lebesgue-Zygmund space $L^p_{\mu,\Psi}$ as the space of all measurable…

We analyze the main properties of the Bergman spaces of weak $L_p$- solutions for a biquaternionic Vekua equation of the form \[ \mathbf{D}w(x)-\mathbf{Q}_Aw(x)=0 \] on bounded domains of $\mathbb{R}^3$, where the operator $\mathbf{Q}_A$…

\begin{abstract} We obtain sharp $L^p\rightarrow L^q$ hypercontractive inequalities for the weighted Bergman spaces on the unit disk $\mathbb{D}$ with the usual weights \\ $\frac{\alpha-1}{\pi}(1-|z|^2)^{\alpha-2},\alpha>1$ for $q\geq 2,$…

Let $\omega$ be a radial weight on the unit disc of the complex plane $\mathbb{D}$ and denote $\omega_x =\int_0^1 s^x \omega(s)\,ds$, $x\ge 0$, for the moments of $\omega$ and $\widehat{\omega}(r)=\int_r^1 \omega(s)\,ds$ for the tail…

The boundedness of the small Hankel operator $h^\omega_{f}(g)=\overline{P_\omega}(fg)$ induced by a measurable symbol $f$ and the Bergman projection $P_\omega$ associated to a radial weight $\omega$ acting from the weighted Bergman space…

The Bergman projection $P_\alpha$, induced by a standard radial weight, is bounded and onto from $L^\infty$ to the Bloch space $\mathcal{B}$. However, $P_\alpha: L^\infty\to \mathcal{B}$ is not a projection. This fact can be emended via the…

It is shown that the radial averaging operator $$ T_\omega(f)(z)=\frac{\int_{|z|}^1f\left(s\frac{z}{|z|}\right)\omega(s)\,ds}{\widehat{\omega}(z)},\quad \widehat{\omega}(z)=\int_{|z|}^1\omega(s)\,ds, $$ induced by a radial weight $\omega$…

An equivalent norm in the weighted Bergman space $A^p_\omega$, induced by an $\omega$ in a certain large class of non-radial weights, is established in terms of higher order derivatives. Other Littlewood-Paley inequalities are also…

Let $A^p_\omega$ denote the Bergman space in the unit disc $\mathbb{D}$ of the complex plane induced by a radial weight $\omega$ with the doubling property $\int_{r}^1\omega(s)\,ds\le C\int_{\frac{1+r}{2}}^1\omega(s)\,ds$. The tent space…

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…

We prove the weighted $L^p$ regularity of the ordinary Bergman and Cauchy-Szeg\H{o} projections on strongly pseudoconvex domains $D$ in $\mathbb{C}^n$ with near minimal smoothness for appropriate generalizations of the $B_p/A_p$ classes. In…

Bounded and compact generalized weighted composition operators acting from the weighted Bergman space $A^p_\omega$, where $0<p<\infty$ and $\omega$ belongs to the class $\mathcal{D}$ of radial weights satisfying a two-sided doubling…

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 $$…

In this paper, we prove the boundedness of the Bergman projection on weighted mixed norm spaces of the upper-half space for some weights that are constructed using the logarithm function and growth functions. Our necessary and sufficient…

In this paper, we characterize the boundedness and compactness of differences of weighted composition operators from weighted Bergman spaces $A^p_\omega$ induced by a doubling weight $\omega$ to Lebesgue spaces $L^q_\mu$ on the unit ball…

This paper is based on the course \lq\lq Weighted Hardy-Bergman spaces\rq\rq\, I delivered in the Summer School \lq\lq Complex and Harmonic Analysis and Related Topics\rq\rq at the Mekrij\"arvi research station of University of Eastern…

We show that weighted Bergman projections corresponding to radially symmetric weights on the unit disc are bounded on Sobolev spaces.