Related papers: Multipliers on $\mathcal{S}_{\omega}(\mathbb{R}^N)…

We prove a general type description result for the multipliers acting between two periodic Bessel potential spaces, defined on the $n$--dimensional torus, in a case when their smoothness indices are of different signs. This is done through…

We characterize, using time-frequency analysis, the continuity and compactness of the Weyl operator in global classes of ultradifferentiable functions $\mathcal{S}_\omega$, for weight functions $\omega$ in the sense of Braun, Meise and…

Let $\omega$ be a non-negative function on $\mathbb{R}$. We are looking for a non-zero $f$ from a given space of entire functions $X$ satisfying $$(a) \quad|f|\leq \omega\text{\quad or\quad(b)}\quad |f|\asymp\omega.$$ The classical…

We continue our investigations on pointwise multipliers for Besov spaces of dominating mixed smoothness. This time we study the algebra property of the classes $S^r_{p,q}B(\mathbb{R}^d)$ with respect to pointwise multiplication. In addition…

We introduce the notion of a pseudomultiplier of a Hilbert space $\mathcal H$ of functions on a set $\Omega$. Roughly, a pseudomultiplier of $\mathcal H$ is a function which multiplies a finite-codimensional subspace of $\mathcal H$ into…

In this paper we study sharp generalizations of $\dot{F}_p^{0,q}$ multiplier theorem of Mikhlin-H\"ormander type. The class of multipliers that we consider involves Herz spaces $K_u^{s,t}$. Plancherel's theorem proves…

We define tensors, corresponding to cubic polynomials, which have the same exponent $\omega$ as the matrix multiplication tensor. In particular, we study the symmetrized matrix multiplication tensor $sM_n$ defined on an $n\times n$ matrix…

We prove that the space of pointwise multipliers between two distinct Musielak--Orlicz spaces is another Musielak-Orlicz space and the function defining it is given by an appropriately generalized Legendre transform. In particular, we…

We make an exhaustive study of the properties of multiplication operator $M_u$ acting on K\"othe spaces. We characterize the multiplication operators, acting on K\"othe spaces, which are: bounded, injective, onto, bijective, Fredholm,…

The aim of this paper is to study the multipliers from $A_{r}(I)$ to $A_{p}(I), r \ne p$, where $I=(0,\infty)$ is the locally compact topological semigroup with multiplication max and usual topology and $A_{r}(I) = \{f \in L_{1}(I)\hbox{:}…

In this paper we study some estimates of norms in variable exponent Lebesgue spaces for maximal multiplier operators.We will consider the case when multiplier is the Fourier transform of a compactly supported Borel measure

It is known that the Sobolev space $L^2_s$ with $s>n/2$ appeared in the H\"ormander multiplier theorem can be replaced by the Besov space $B^{2,1}_{n/2}$. On the other hand, the Besov space $B_{n/2}^{2,1}$ is continuously embedded in the…

Let $\Phi_1 , \Phi_2 $ and $ \Phi_3$ be Young functions and let $L^{\Phi_1}(\mathbb{R})$, $L^{\Phi_2}(\mathbb{R})$ and $L^{\Phi_3}(\mathbb{R})$ be the corresponding Orlicz spaces. We say that a function $m(\xi,\eta)$ defined on…

In this paper we are concerned with two classes of conformally invariant spaces of analytic functions in the unit disc $\D$, the Besov spaces $B^p$ $(1\le p<\infty )$ and the $Q_s$ spaces $(0<s<\infty )$. Our main objective is to…

We study multiplier theorems on a vector-valued function space, which is a generalization of the results of Calder\'on-Torchinsky and Grafakos-He-Honz\'ik-Nguyen, and an improvement of the result of Triebel. For $0<p<\infty$ and $0<q\leq…

Consider the multidimensional Bessel operator $$B f(x) = -\sum_{j=1}^N \left(\partial_j^2 f(x) +\frac{\alpha_j}{x_j} \partial_j f(x)\right), \quad x\in(0,\infty)^N. $$ Let $d = \sum_{j=1}^N \max(1,\alpha_j+1)$ be the homogeneous dimension…

The space ${\mathcal A}$ of almost complex structures on a closed manifold $M$ is studied. A natural parametrization of the space ${\mathcal A}$ is defined. It is shown, that ${\mathcal A}$ is a infinite dimensional complex weak…

We prove $L^{p}$-boundedness of oscillating multipliers on all symmetric spaces and a class of locally symmetric spaces.

Given an n-tuple of multiplication operators on the Bergman space of a bounded pseudoconvex domain in C^n, we study the algebra of their commutants. In particular, we give a geometric description of the maximal C*-subalgebra of this…

We study weighted $(PLB)$-spaces of ultradifferentiable functions defined via a weight function (in the sense of Braun, Meise and Taylor) and a weight system. We characterize when such spaces are ultrabornological in terms of the defining…