Related papers: Weighted Bergman spaces induced by rapidly incresi…

We study certain weighted area integral means of analytic functions in the unit disc. We relate the growth of these means to the property of being mean H\"older continuous with respect to the Bergman space norm. In contrast with earlier…

The main objective of this work is to bring together two well known and, a priori, unrelated theories dealing with weighted inequalities for the Hardy-Littlewood maximal operator $M$, and thus, we consider the boundedness of $M$ in the…

We introduce new weighted $L^p$-type spaces defined in terms of weight function matrices and characterize the inclusion relations in terms of the defining matrices. Moreover, we provide a detailed study concerning the coincidence with the…

We prove that for every $p\ge 1$ there exists a bounded function in the analytic Besov space $B^p$ whose derivative is "badly integrable", along every radius. We apply this result to study multipliers and weighted superposition operators…

Given a regular weight $\omega$ and a positive Borel measure $\mu$ on the unit disc $\mathbb{D}$, the Toeplitz operator associated with $\mu$ is $$ \mathcal{T}_\mu(f)(z)=\int_{\mathbb{D}} f(\zeta)\bar{B_z^\omega(\zeta)}\,d\mu(\zeta), $$…

We show that the Korenblum maximum (domination) principle is valid for weighted Bergman spaces $A^p_w$ with arbitrary (non-negative and integrable) radial weights $w$ in the case $1\le p<\infty$. We also notice that in every weighted…

In a note published in 1925, G. H. Hardy stated the inequality \begin{equation*} \sum_{n=1}^\infty \left(\frac{1}{n}\sum_{k=1}^n a_k \right)^p \leq \left(\frac{p}{p-1}\right)^p \sum_{n=1}^\infty a_n^p, \end{equation*} for any non-negative…

We investigate the higher-order Volterra-type integral operator $T_{g,n}$ on the unit disk, defined for $n\in\mathbb N$ by \[ T_{g,n}[f](z) := \underbrace{\int_{0}^{z}\int_{0}^{t_1}\cdots\int_{0}^{t_{n-1}}}_{n\ \text{times}}…

After a review of the reproducing kernel Banach space framework and semi-inner products, we apply the techniques to the setting of Hardy spaces $H^p$ and Bergman spaces $A^p$, $1<p<\infty$, on the unit ball in $\mathbb{C}^n$, as well as the…

Let $\mu$ be a positive Borel measure on the interval [0,1). The Hankel matrix $\mathcal{H}_\mu= (\mu_{n,k})_{n,k\geq0}$ with entries $\mu_{n,k}= \mu_{n+k}$, where $\mu_n=\int_{ [0,1)}t^nd\mu(t)$, induces formally the operator…

We obtain characterizations of positive Borel measures $\mu$ on $\B^n$ so that some weighted Hardy-Sobolev are imbedded in $L^p(d\mu)$, where $w$ is an $A_p$ weight in the unit sphere of $\C^n$.

The boundedness and compactness of weighted composition operators on the Hardy space ${\mathcal H}^2$ of the unit disc is analysed. Particular reference is made to the case when the self-map of the disc is an inner function. Schatten-class…

The classical Korenblum-Roberts Theorem characterizes the cyclic singular inner functions in the Bergman spaces of the unit disk $\mathbb{D}$ as those for which the corresponding singular measure vanishes on Beurling-Carleson sets of…

Let $\mathcal{D}$ be the class of radial weights on the unit disk which satisfy both forward and reverse doubling conditions. Let $g$ be an analytic function on the unit disk $\mathbb{D}$. We characterize bounded and compact Volterra type…

Let $s\in{\mathbb R}$, $q\in (0,\infty]$, and $\tau\in[0,\infty)$. It is well known that Besov-type spaces $\dot B^{s,\tau}_{p,q}$ with $p\in (0,\infty]$ and Triebel--Lizorkin-type spaces $\dot F^{s,\tau}_{p,q}$ with $p\in (0,\infty)$ when…

Let $0<p<\infty$, $\beta>-1$, and $\Omega$ be a strongly pseudoconvex bounded domain with a smooth boundary in $\mathbb{C}^n$. We will study the interpolation problem for weighted Bergman spaces $A^p_\beta(\Omega)$. In the case, $1\leq…

This paper investigates the essential norm of Toeplitz operators $\mathcal{T}_\mu$ acting from the Bergman space $A_\omega^p$ to $A_\omega^q$ ($1 < p \leq q < \infty$) on the unit ball, where $\mu$ is a positive Borel measure and $\omega…

We characterize the Carleson measures $\mu$ on the unit disk for which the image of the Hardy space $H^p$ under the corresponding embedding operator is closed in $L^p(\mu)$. In fact, a more general result involving $(p,q)$-Carleson measures…

In this paper, for $p\in(1,\infty)$ we study $p$-complete boundedness of weighted homomorphisms on the $p$-analog of the Fourier-Stieltjes algebras, $B_p(G)$, based on the $p$-operator space structure defined by the authors. Here, for a…

In the present paper we study embedding operators for weighted Sobolev spaces whose weights satisfy the well-known Muckenhoupt A_p-condition. Sufficient conditions for boundedness and compactness of the embedding operators are obtained for…