Related papers: On a particular integral operator
We investigate composition-differentiation operators acting on the Dirichlet space of the unit disk. Specifically, we determine characterizations for bounded, compact, and Hilbert-Schmidt composition-differentiation operators. In addition,…
We study mapping properties of two-dimensional linear integral operators in some weighted spaces with special kernels. The considered spaces are certain variant of Sobolev--Slobodetskii spaces and their generalizations related to Banach…
In this paper, we give the necessary and sufficient conditions for the boundedness of fractional integral operators on the modulation spaces.
We introduce a suitable notion of integral operators (comprising the fractional Laplacian as a particular case) acting on functions with minimal requirements at infinity. For these functions, the classical definition would lead to divergent…
Functional analysis, especially the theory of Hilbert spaces and of operators on these, form an important area in mathematics. We formalized the Isabelle/HOL library Complex_Bounded_Operators containing a large amount of theorems about…
We show that some previous results concerning the boundedness of differentiation and integration operators on weighted spaces given by radial weights in the unit disk or the complex plane might fail without some natural additional…
We work with very general Banach spaces of analytic functions in the disk or other domains which satisfy a minimum number of natural axioms. Among the preliminary results, we discuss some implications of the basic axioms and identify all…
We consider composition operators in the Dirichlet space of the unit disc in the plane. Various criteria on boundedness, compactness and Hilbert-Schmidt class membership are established. Some of these criteria are shown to be optimal.
We study composition operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm and the essential norm. In addition, we study the isometric…
In this note, we study the boundedness of integral operators $I_{g}$ and $T_{g}$ on analytic Morrey spaces. Furthermore, the norm and essential norm of those operators are given.
We study power boundedness and related properties such as mean ergodicity for (weighted) composition operators on function spaces defined by local properties. As a main application of our general approach we characterize when (weighted)…
It is proved that both oscillatory integral operators and fractional oscillatory integral operators are bounded on weighted Morrey spaces. The corresponding commutators generated by $BMO$ functions are also considered.
We investigate the numerical ranges of weighted composition operators on weighted Dirichlet spaces, focusing on the properties of the inducing functions. We identify conditions on these functions under which the origin lies in the interior…
We consider various systematic ways of defining unbounded operator valued integrals of complex functions with respect to (mostly) positive operator measures and positive sesquilinear form measures, and investigate their relationships to…
We characterize bounded, compact, and Hilbert-Schmidt composition-differentiation operators on weighted Dirichlet spaces. The essential norm is estimated via the asymptotic behavior of a function that involves the generalized Nevanlinna…
We investigate some types of composition operators, linear and not, and conditions for some spaces to be mapped into themselves and for the operators to satisfy some good properties.
We consider weighted composition operators, that is operators of the type $g \mapsto w \cdot g \circ f$, acting on spaces of Lipschitz functions. Bounded weighted composition operators, as well as some compact weighted composition…
This paper aims to characterize boundedness of composition operators on Besov spaces $B^s_{p,q}$ of higher order derivatives $s>1+1/p$ on the one-dimensional Euclidean space. In contrast to the lower order case $0<s<1$, there were a few…
We construct a Weyl pseudodifferential calculus tailored to studying boundedness of operators on weighted $L^p$ spaces over $\mathbb{R}^d$ with weights of the form $\exp(-\phi(x))$, for $\phi$ a $C^2$ function, a setting in which the…
In this note we consider weighted conditional type operators between different Orlicz spaces and generalized conditional type Holder inequality that we defined in [2]. Then we give some necessary and sufficient conditions for boundedness of…