Related papers: Viewing *-multiplication operators between Orlics …

Conditions for a function (number sequence) to be a multiplier on the space of integrable functions on $\Bbb R$ ($\Bbb T$) are given. This generalizes recent results of Giang and Moricz.

We prove novel results on interpolation of Fredholm operators including an abstract factorization theorem. The main result of this paper provides sufficient conditions on the parameters $\theta \in (0,1)$ and $q\in \lbrack 1,\infty ]$ under…

We study multipliers of Hardy-Orlicz spaces $\mH_{\Phi}$ which are strictly contained between $\bigcup_{p>0}H^p$ and so-called ``big'' Hardy-Orlicz spaces. Big Hardy-Orlicz spaces, carrying an algebraic structure, are equal to their…

Let $L=-\Delta +|x|^2$ be the Hermite operator on $\mathbb{R}^n$, and $T$ be a Calder\'on-Zygmund type operator that is modelled on certain singular integrals related to $L$. We establish necessary and sufficient conditions for $T$ to be…

For $\mathbb B^n$ the unit ball of $\mathbb C^n$, we consider Bergman-Orlicz spaces of holomorphic functions in $L^\Phi_\alpha$, which are generalizations of classical Bergman spaces. We characterize the dual space of large Bergman-Orlicz…

Following several papers in the prior literature, we study the relationship between order bounded operators, topologically bounded operators and topologically continuous operators. Our main contribution is two folded: (i) we provide a set…

We show that the Dirac operator on a compact globally hyperbolic Lorentzian spacetime with spacelike Cauchy boundary is a Fredholm operator if appropriate boundary conditions are imposed. We prove that the index of this operator is given by…

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…

We study the range of time-frequency localization operators acting on modulation spaces and prove a lifting theorem. As an application we also characterize the range of Gabor multipliers, and, in the realm of complex analysis, we…

We deduce continuity properties for pseudo-differential operators with symbols in Orlicz modulation spaces when acting on other Orlicz modulation spaces. In particular we extend well-known results in the literature. We also show that the…

Let $E$ be a Banach function space on a probability measure space $(\Omega ,\Sigma,\mu).$ Let $X$ be a Banach space and $E(X)$ be the associated K\"{o}the-Bochner space. An operator on $E(X)$ is called a multiplication operator if it is…

Let $\lambda$ be a complex number in the closed unit disc $\overline{\Bbb D}$, and $\cal H$ be a separable Hilbert space with the orthonormal basis, say, ${\cal E}=\{e_n:n=0,1,2,\cdots\}$. A bounded operator $T$ on $\cal H$ is called a…

We prove that the existence of a Mihlin-H\"ormander functional calculus for an operator $L$ implies the boundedness on $L^p$ of both the maximal operators and the continuous square functions build on spectral multipliers of $L.$ The…

The purpose of this paper is to establish some neccessary and sufficient conditions for the boundedness of a general class of multilinear Hausdorff operators that acts on the product of some two weighted function spaces such as the two…

We introduce unbounded multipliers on operator spaces. These multipliers generalize both, regular operators on Hilbert C*-modules and (bounded) multipliers on operator spaces.

We consider an integral operator $\mathcal{I}$, special instances of which was studied in various contexts. Using an appropriate transformation we write this operator in terms of weighted composition operators. Then, we provide a…

We study the Hardy-Littlewood maximal operator in the Musielak-Orlicz-Sobolev space $W^{1,\varphi}(\mathbb{R}^n)$. Under some natural assumptions on $\varphi$ we show that the maximal function is bounded and continuous in…

We compute the essential norm of inclusion operators, composition operators and multipliers acting from a closed subspace of some $L^p$-space into a subspace of some $L^q$-space, with $p > q.$

We study mapping properties of the centered Hardy--Littlewood maximal operator $\mathcal{M}$ acting on Lorentz spaces $L^{p,q}(\mathfrak{X})$ in the context of certain non-doubling metric measure spaces $\mathfrak{X}$. The special class of…

In a class of inner product H\"ormander spaces, we investigate a general elliptic problem for which the maximum of orders of boundary conditions is grater than or equal to the order of elliptic equation. The order of regularity for these…