相关论文: Properties of $\beta$-Ces\`aro operators on $\alph…

We introduce the Banach spaces $\ell^p_{a,b}$ and $c_{0,a,b}$, of analytic functions on the unit disc, having normalized Schauder bases consisting of polynomials of the form $f_n(z)=(a_n+b_nz)z^n, ~~n\geq0$, where $\{f_n\}$ is assumed to be…

Assume that $\Delta$ is the open unit disk in the complex plane and $\mathcal{A}$ is the class of normalized analytic functions in $\Delta$. In this paper we introduce and study the class \begin{equation*} \mathcal{BS}(\alpha):=\left\{f\in…

This article reviews several definitions of the fractional Laplace operator (-Delta)^{alpha/2} (0 < alpha < 2) in R^d, also known as the Riesz fractional derivative operator, as an operator on Lebesgue spaces L^p, on the space C_0 of…

In this paper, we investigate the boundedness and compactness of generalized integration operators $T_g^{n,k}$ and $S_g^{n,0}$ from analytic tent spaces $AT_p^\infty(\alpha)$ to $AT_q^\infty(\beta)$ when $0<p,q<\infty,\alpha,\beta>-2$.

In this work, the mixed Schwarz inequality for semi-Hilbertian space operators is proved. Namely, for every positive Hilbert space operator $A$. If $f$ and $g$ are nonnegative continuous functions on $\left[0,\infty\right)$ satisfying…

For 0 < s < 1, let phi_s(z)=sz+(1-s). We investigate the unital C*-algebra generated by the semigroup {C_{phi_s} : 0 < s < 1} of composition operators acting on the Hardy space of the unit disk. We determine the joint approximate point…

We consider Hilbert spaces of analytic functions in the disk with a normalized reproducing kernel and such that the backward shift $f(z) \mapsto \frac{f(z)-f(0)}{z}$ is a contraction on the space. We present a model for this operator and…

In this paper, we introduce the concept of cb-frames for operator spaces. We show that there is a concrete cb-frame for the reduced free group C*-algebra $C_r^*(F_2)$, which is derived from the infinite convex decomposition of the…

We study the asymptotic behaviour of orbits $(T^nx)_{n\ge0}$ of the classical Ces\`aro operator $T$ for sequences $x$ in the Banach space $c$ of convergent sequences. We give new non-probabilistic proofs, based on the Katznelson-Tzafriri…

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 $$…

We study harmonic Besov spaces $b^p_\alpha$ on the unit ball of $\mathbb{R}^n$, where $0<p<1$ and $\alpha\in\mathbb{R}$. We provide characterizations in terms of partial and radial derivatives and certain radial differential operators that…

Let $\mathcal{T}^*$ be the semi-group maximal function associated to the Schr\"odinger operator $-\Delta+V(x)$ with $V$ satisfying an appropriate reverse H\"{o}lder inequality. In this paper, we show that the commutator of $\mathcal{T}^*$…

Let {\phi} be an analytic self-map of D and be an analytic operator-valued function on D, where D is the unit disk. We provide necessary and sufficient conditions for the boundedness and compactness of weighted composition operators…

Let $A$ be a unital Banach algebra. We give a characterization of the left Banach $A$-modules $X$ for which there exists a commutative unital $C^*$-algebra $C(K)$, a linear isometry $i\colon X\to C(K)$, and a contractive unital homomorphism…

In this article, we characterize the radial operators on weighted Bergman spaces of Reinhardt domains in $\mathbb{C}^n$, the Dirichlet and the Hardy spaces of the open unit disk $\mathbb{D}$, in terms of integral representations. We also…

Let $H(\mathbb{B})$ denote the space of all holomorphic functions on the unit ball $\mathbb{B}\in \mathbb{C}^n$. In this paper we investigate the boundedness and compactness of the products of radial derivative operator and the following…

In this article, we characterize the Beurling and Model subspaces of the Hardy-Hilbert space $H^2(\mathbb{D})$ invariant under the composition operator $C_{\phi_a}f=f\circ\phi_a$, where $\phi_a(z) = az + 1 - a$ for $a \in (0,1)$ is an…

We show that the classical Szasz analytic function $S_N(f)(x)$ is obtained by applying the pseudo-differential operator $f(N^{-1}D_{\theta})$ to the Bergman kernels for the Bargmann-Fock space. The expression generalizes immediately to any…

For $\alpha, \beta \in L^{\infty} (S^1),$ the singular integral operator $S_{\alpha,\beta}$ on $L^2 (S^1)$ is defined by $S_{\alpha,\beta}f:= \alpha Pf+\beta Qf$, where $P$ denotes the orthogonal projection of $L^2(S^1)$ onto the Hardy…

Denote by $[0,\omega_1)$ the set of countable ordinals, equipped with the order topology, let $L_0$ be the disjoint union of the compact ordinal intervals $[0,\alpha]$ for $\alpha$ countable, and consider the Banach spaces $C_0[0,\omega_1)$…