A full description of the membership in the Schatten ideal $S_p\left(A{²}_{\omega }\right)$ for 0 < p < ∞ of Toeplitz operators acting on large weighted Bergman spaces is obtained.

We consider a complete connected noncompact Riemannian manifold M with bounded geometry and spectral gap. We prove that the imaginary powers of the Laplacian and the Riesz transform are bounded from the Hardy space X¹(M), introduced in previous work of the authors, to L¹(M).

The Hardy spaces of Dirichlet series, denoted by ${}^p$ (p ≥ 1), have been studied by Hedenmalm et al. (1997) when p = 2 and by Bayart (2002) in the general case. In this paper we study some $L^p$-generalizations of spaces of Dirichlet series, particularly two families of Bergman spaces, denoted ${}^p$ and ${ℬ}^p$. Each could appear as a “natural” way to generalize the classical case of the unit disk. We recover classical properties of spaces of analytic functions: boundedness of point evaluation, embeddings between...

We study the reproducing kernel Hilbert space with kernel kd , where d is a positive integer and k is the reproducing kernel of the analytic Dirichlet space.

We prove some optimal estimates of Hölder-logarithmic type in the Hardy-Sobolev spaces $H^{k,p}\left(G\right)$, where $k\in {\mathbb{N}}^{*}$, $1\le p\le \infty$ and $G$ is either the open unit disk $𝔻$ or the annular domain $G_s$, $0<s<1$ of the complex space $ℂ$. More precisely, we study the behavior on the interior of $G$ of any function $f$ belonging to the unit ball of the Hardy-Sobolev spaces $H^{k,p}\left(G\right)$ from its behavior on any open connected subset $I$ of the boundary $\partial G$ of $G$ with respect to the $L^1$-norm. Our results can be viewed as an improvement and generalization of those established...

Let $\varphi$ be an entire self-map of ${ℂ}^N$, $u_0$ be an entire function on ${ℂ}^N$ and $𝐮=(u_1,\cdots ,u_N)$ be a vector-valued entire function on ${ℂ}^N$. We extend the Stević-Sharma type operator to the classcial Fock spaces, by defining an operator $T_{u_0,𝐮,\varphi }$ as follows: $$-.4pt{T}_{u_0,𝐮,\varphi }f=u_0·f\circ \varphi +\sum _{i=1}^N{u}_i·\frac{\partial f}{\partial z_i}\circ \varphi .$$ We investigate the boundedness and compactness of $T_{u_0,𝐮,\varphi }$ on Fock spaces. The complex symmetry and self-adjointness of $T_{u_0,𝐮,\varphi }$ are also characterized.

Let HE∞ be the space of all bounded holomorphic functions on the unit ball of the Banach space E. In this note we study the algebra homomorphisms on HE∞ which are strict continuous.