## 51 Citations

### Toeplitz Operators on Weighted Bergman Spaces Induced by a Class of Radial Weights

- 2022

Mathematics

The Journal of Geometric Analysis

Suppose that $$\omega $$ ω is a radial weight on the unit disk that satisfies both forward and reverse doubling conditions. Using Carleson measures and T 1-type conditions, we obtain necessary and…

### GENERALISED WEIGHTED COMPOSITION OPERATORS ON BERGMAN SPACES INDUCED BY DOUBLING WEIGHTS

- 2021

Mathematics

Bulletin of the Australian Mathematical Society

Abstract We characterise bounded and compact generalised weighted composition operators acting from the weighted Bergman space
$A^p_\omega $
, where
$0<p<\infty $
and
$\omega $
belongs to the…

### Compact differences of weighted composition operators

- 2020

Mathematics

Collectanea Mathematica

Compact differences of two weighted composition operators acting from the weighted Bergman space $$A^p_{\omega }$$ A ω p to another weighted Bergman space $$A^q_{\nu }$$ A ν q , where $$0<p\le…

### Atomic Decomposition and Carleson Measures for Weighted Mixed Norm Spaces

- 2019

Mathematics

The Journal of Geometric Analysis

The purpose of this paper is to establish an atomic decomposition for functions in the weighted mixed norm space $$A^{p,q}_\omega $$ A ω p , q induced by a radial weight $$\omega $$ ω in the unit…

### On the Bergman projections acting on $L^\infty$ in the unit ball $\mathbb B_n$

- 2019

Mathematics

Given a weight function, we define the Bergman type projection with values in the corresponding weighted Bergman space on the unit ball $\mathbb B_n$ of $\mathbb C^n, n>1$. We characterize the radial…

### Toeplitz operators on the weighted Bergman spaces

- 2020

Mathematics

In this paper, we first study Toeplitz operators on a weighted Bergman space $L_a^1(\omega)$ where the weight $\omega$ is regular. Using the Carleson measure and $T1$-type condition, we obtain…

### Harmonic conjugates on Bergman spaces induced by doubling weights

- 2020

Mathematics

Analysis and Mathematical Physics

A radial weight $$\omega $$ ω belongs to the class $$\widehat{\mathcal {D}}$$ D ^ if there exists $$C=C(\omega )\ge 1$$ C = C ( ω ) ≥ 1 such that $$\int _r^1 \omega (s)\,ds\le C\int…

### Radial Two Weight Inequality for Maximal Bergman Projection Induced by a Regular Weight

- 2020

Mathematics

Potential Analysis

It is shown in quantitative terms that the maximal Bergman projection P ω + ( f ) ( z ) = ∫ D f ( ζ ) | B z ω ( ζ ) | ω ( ζ ) d A ( ζ ) , $$ {P}^{+}_{\omega}(f)(z)={\int}_{\mathbb{D}}…

### Besov Spaces Induced by Doubling Weights

- 2020

Mathematics

Constructive Approximation

Let $$1\leqslant p<\infty $$ 1 ⩽ p < ∞ , $$0<q<\infty $$ 0 < q < ∞ , and $$\nu $$ ν be a two-sided doubling weight satisfying $$\begin{aligned} \sup _{0\leqslant r<1}\frac{(1-r)^q}{\int _r^1\nu…

### Bergman projection and BMO in hyperbolic metric -- improvement of classical result

- 2022

Mathematics

. The Bergman projection P α , induced by a standard radial weight, is bounded and onto from L 8 to the Bloch space B . However, P α : L 8 Ñ B is not a projection. This fact can be emended via the…

## 36 References

### Weighted Bergman spaces induced by rapidly incresing weights

- 2012

Mathematics

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}
…

### On the boundedness of Bergman projection

- 2015

Mathematics

The main purpose of this survey is to gather results on the boundedness of the Bergman projection. First, we shall go over some equivalent norms on weighted Bergman spaces $A^p_\omega$ which are…

### Harmonic conjugates on Bergman spaces induced by doubling weights

- 2020

Mathematics

Analysis and Mathematical Physics

A radial weight $$\omega $$ ω belongs to the class $$\widehat{\mathcal {D}}$$ D ^ if there exists $$C=C(\omega )\ge 1$$ C = C ( ω ) ≥ 1 such that $$\int _r^1 \omega (s)\,ds\le C\int…

### Small weighted Bergman spaces

- 2015

Mathematics

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…

### Radial Two Weight Inequality for Maximal Bergman Projection Induced by a Regular Weight

- 2020

Mathematics

Potential Analysis

It is shown in quantitative terms that the maximal Bergman projection P ω + ( f ) ( z ) = ∫ D f ( ζ ) | B z ω ( ζ ) | ω ( ζ ) d A ( ζ ) , $$ {P}^{+}_{\omega}(f)(z)={\int}_{\mathbb{D}}…

### UNBOUNDEDNESS OF THE BERGMAN PROJECTIONS ON $L^{p}$ SPACES WITH EXPONENTIAL WEIGHTS

- 2004

Mathematics, Philosophy

Proceedings of the Edinburgh Mathematical Society

Abstract We prove that the Bergman projection on $L^p(w)$ $(p\neq 2)$, where $w(r)=(1-r^2)^A\textrm{e}^{-B/(1-r^2)^{\alpha}}$, is not bounded. AMS 2000 Mathematics subject classification: Primary…

### $L^{p}$-behaviour of the integral means of analytic functions

- 1984

Mathematics

Various results on LP·behaviour of power series with positive coeffi dents are extended to Lipschitz spaces. For example, we have a characterization (decomposition) of these spaces, which enables us…