The purpose of this paper is to study the Sarason’s problem on Fock spaces of polyanalytic functions. Namely, given two polyanalytic symbols $f$ and $g$, we establish a necessary and sufficient condition for the boundedness of some Toeplitz products $T_f{T}_{\overline{g}}$ subjected to certain restriction on $f$ and $g$. We also characterize this property in terms of the Berezin transform.

In this paper we study spaces of holomorphic functions on the right half-plane R, that we denote by Mpω, whose growth conditions are given in terms of a translation invariant measure ω on the closed half-plane R. Such a measure has the form ω = ν ⊗ m, where m is the Lebesgue measure on R and ν is a regular Borel measure on [0, +∞). We call these spaces generalized Hardy–Bergman spaces on the half-plane R. We study in particular the case of ν purely atomic, with point masses on an arithmetic progression...

We present sufficient conditions for the existence of $p$th powers of a quasihomogeneous Toeplitz operator $T_{{\mathrm{e}}^{\mathrm{i}s\theta }\psi }$, where $\psi$ is a radial polynomial function and $p$, $s$ are natural numbers. A large class of examples is provided to illustrate our results. To our best knowledge those examples are not covered by the current literature. The main tools in the proof of our results are the Mellin transform and some classical theorems of complex analysis.

We present a proof of the weighted estimate of the Bergman projection that does not use extrapolation results. This estimate is extended to product domains using an adapted definition of Békollé-Bonami weights in this setting. An application to bounded Toeplitz products is also given.

Let $\varphi$ be an analytic self-mapping of $𝔻$ and $g$ an analytic function on $𝔻$. In this paper we characterize the bounded and compact Volterra composition operators from the Bergman-type space to the Bloch-type space. We also obtain an asymptotical expression of the essential norm of these operators in terms of the symbols $g$ and $\varphi$.

Let ϕ: → and ψ: → ℂ be analytic maps. They induce a weighted composition operator $\psi C_{\varphi }$ acting between weighted Bergman spaces of infinite order and weighted Bloch type spaces. Under some assumptions on the weights we give a characterization for such an operator to be bounded in terms of the weights involved as well as the functions ψ and ϕ