Related papers: Schatten classes of generalized Hilbert operators

Let $m\in\mathbb N$, $P(D):=\sum_{|\alpha|=2m}(-1)^m a_\alpha D^\alpha$ be a $2m$-order homogeneous elliptic operator with real constant coefficients on $\mathbb{R}^n$, and $V$ a measurable function on $\mathbb{R}^n$. In this article, the…

In this paper we present symbolic criteria for invariant operators on compact topological groups $G$ characterising the Schatten-von Neumann classes $S_{r}(L^{2}(G))$ for all $0<r\leq\infty$. Since it is known that for pseudo-differential…

Let $\mu$ be a positive Borel measure on the positive real axis. We study the integral operator $$ \mathcal{H}_{\mu}(f)(z)=\int_{0}^{\infty}\frac{1}{t}f\left(\frac{z}{t}\right)\,d\mu(t),\quad z\in \mathbb{C}\,, $$ acting on the Fock spaces…

Let $T\colon H\to H$ be a bounded operator on Hilbert space. We say that $T$ has a polygonal type if there exists an open convex polygon $\Delta\subset {\mathbb D}$, with $\overline{\Delta}\cap{\mathbb T}\neq\emptyset$, such that the…

Schatten-Herz class Toeplitz operators on weighted Bergman spaces induced by doubling weights are investigated in this paper.

We characterize boundedness and compactness of Toeplitz operators on large vector-valued Fock spaces with Dall'Ara's weights [Adv.\ Math., 285 (2015) 1706--1740] in terms of generalized Berezin transforms, averaging functions, and Carleson…

In this article, we look for the weight functions (say $g$) that admits the following generalized Hardy-Rellich type inequality: $ \int_{\Omega} g(x) u^2 dx \leq C \int_{\Omega} |\Delta u|^2 dx, \forall u \in \mathcal{D}^{2,2}_0(\Omega), $…

Let (E,H,mu) be an abstract Wiener space and let D_V := VD, where D denotes the Malliavin derivative and V is a closed and densely defined operator from H into another Hilbert space G. Given a bounded operator B on G, coercive on the…

Let $\mu$ be a positive Borel measure on $[0,1)$. If $f \in H(\mathbb{D})$ and $\alpha>-1$, the generalized integral type Hilbert operator defined as follows: $$\mathcal{I}_{\mu_{\alpha+1}}(f)(z)=\int^1_{0}…

In this work we establish sharp kernel conditions ensuring that the corresponding integral operators belong to Schatten-von Neumann classes. The conditions are given in terms of the spectral properties of operators acting on the kernel. As…

We link Sogge's type $L^p$-estimates for eigenfunctions of the Laplacian on compact manifolds with the problem of providing criteria for the $r$-nuclearity of Fourier integral operators. The classes of Fourier integral operators…

Bounded and compact generalized weighted composition operators acting from the weighted Bergman space $A^p_\omega$, where $0<p<\infty$ and $\omega$ belongs to the class $\mathcal{D}$ of radial weights satisfying a two-sided doubling…

Let $\mu$ be a positive Borel measure on the interval $[0,1)$. For $\gamma>0$, the Hankel matrix $\mathcal{H}_{\mu,\gamma}=(\mu_{n,k})_{n,k\geq0}$ with entries $\mu_{n,k}=\mu_{n+k}$, where $\mu_{n+k}=\int_{0}^{\infty}t^{n+k}d\mu(t)$.…

Several unitarily invariant norm inequalities and numerical radius inequalities for Hilbert space operators are studied. We investigate some necessary and sufficient conditions for the parallelism of two bounded operators. For a finite rank…

In this paper, the $L^p_v(\R)$-boundedness of the Dunkl-Hausdorff operator $\displaystyle H_{\al,\phi} f(x)=\ent\frac{ |\phi(t)|}{|t|^{2\al+2}}f\lf(\frac{x}{t}\rh) dt $ has been characterized and for a certain type of weight $v$, the…

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…

We consider Schatten class membership of Hankel operators on Paley--Wiener spaces of convex $\Omega \subset \mathbb{R}^n$, both for bounded and unbounded domains. In particular, the classical product Hardy spaces fit within our theory. For…

This paper uses frame techniques to characterize the Schatten class properties of integral operators. The main result shows that if the coefficients of certain frame expansions of the kernel of an integral operator are in (\ell^{2,p}), then…

We establish the following results on higher order $\mathcal{S}^p$-differentiability, $1<p<\infty$, of the operator function arising from a continuous scalar function $f$ and self-adjoint operators defined on a fixed separable Hilbert…

In this article we study the generalized Hilbert matrix operator $\Gamma_\mu$ acting on the Bergman spaces $A^p$ of the unit disc for $1\leq p<\infty$. In particular, we characterize the measures $\mu$ for which the operator $\Gamma_\mu$ is…