相关论文: Two Predualities and Three Operators over Analytic…

We prove that pseudo-differential operators with symbols in the class $S_{1,\delta}^0$ ($0<\delta<1$) are not always bounded on the modulation space $M^{p,q}$ ($q\neq2$).

We study composition operators on spaces of double Dirichlet series, focusing our interest on the characterization of the composition operators of the space of bounded double Dirichlet series $\HCdos$. We also show how the composition…

In this paper, we carry on with the study of the Hardy-Amalgam spaces $\mathcal{H}_{\mathrm{loc}}^{(q,p)}$ spaces introduced in \cite{AbFt}. We investigate their dual spaces and establish some results of boundedness of pseudo-differential…

Two problems are posed that involve the star-invariant subspace $K^p_\theta$ (in the Hardy space $H^p$) associated with an inner function $\theta$. One of these asks for a characterization of the extreme points of the unit ball in…

We examine translation invariant operators on the Polyanalytic Sobolev-Fock spaces and show that they take the form \begin{align*} S_{\phi} F(z) = \int_{\mathbb{C}^n} F(w)e^{\pi z\cdot \overline{w}}\phi(w-z,\overline{w}-z) e^{\pi |w|^2}\,…

We establish a spectral duality for certain unbounded operators in Hilbert space. The class of operators includes discrete graph Laplacians arising from infinite weighted graphs. The problem in this context is to establish a practical…

Over n-dimensional manifolds, I classify ternary differential operators acting on the spaces of weighted densities and invariant with respect to the Lie algebra of vector fields. For n=1, some of these operators can be expressed in terms of…

We consider three problems connected with coinvariant subspaces of the backward shift operator in Hardy spaces $H^p$: 1) properties of truncated Toeplitz operators; 2) Carleson-type embedding theorems for the coinvariant subspaces; 3)…

Any bounded linear operator $ T $ on $ L^2(\mathbb{R}^n) $ gives rise to the operator $ S= B \circ T \circ B^\ast $ on the Fock space $ \mathcal{F}(\C^n) $ where $ B $ is the Bargmann transform. In this article we identify those $ S $ which…

Some new characterizations on Carleson measures for weighted Bergman spaces on the unit ball involving product of functions are obtained. For these we characterize bounded and compact Toeplitz operators between weighted Bergman spaces. The…

For a bounded analytic function $\varphi$ on the unit disk $\D$ with $\|\varphi\|_\infty\le1$ we consider the defect operators $D_\varphi$ and $D_{\overline\varphi}$ of the Toeplitz operators $T_\varphi$ and $T_{\overline\varphi}$,…

In this article, we impose a new class of fractional analytic functions in the open unit disk. By considering this class, we define a fractional operator, which is generalized Salagean and Ruscheweyh differential operators. Moreover, by…

We continue our study of operator algebras with contractive approximate identities (cais). In earlier papers we have introduced and studied a new notion of positivity in operator algebras, with an eye to extending certain $C^*$-algebraic…

In this paper, we provide a complete characterization of bounded Toeplitz operators $T_f$ on the harmonic Bergman space of the unit disk, where the symbol $f$ has a polar decomposition truncated above, that commute with $T_{z+\bar{g}}$, for…

Let denote by $S(\phi)$ the extremal operator defined by the compression of the unilateral shift $S$ to the model subspace $ H(\phi)=H^{2} \ominus \phi H^{2} $ as the following $S(\phi)f(z)=P(zf(z)),$ where $P$ denotes the orthogonal…

We shall present examples of Schauder bases in the preduals to the hyperfinite factors of types $\hbox{II}_1$, $\hbox{II}_\infty$, $\hbox{III}_\lambda$, $0 < \lambda \leq 1$. In the semifinite (respectively, purely infinite) setting, these…

Firstly we establish a sharp pointwise estimate for the arbitrary derivative of the function $f\in F_{\alpha}^{p},$ where $F_{\alpha}^{p}$ denotes the Fock space for $1\leq p<\infty.$ Then, in a particular Hilbert case when $p=2$ we…

Summarizing basic facts from abstract topological modules over Colombeau generalized complex numbers we discuss duality of Colombeau algebras. In particular, we focus on generalized delta functionals and operator kernels as elements of dual…

The bidual of the closure of smooth functions with respect to the Morrey norm coincides with the Morrey space. This assertion is generalized to some Muckenhoupt weighted Morrey spaces. We combine this fact with basic extrapolation…

We establish complete characterizations of various notions of expansivity for weighted composition operators on a very general class of locally convex spaces of continuous functions. This class includes several classical classes of…