Related papers: Optimal extension of the Fourier transform and con…

We introduce partially defined Schur multipliers and obtain necessary and sufficient conditions for the existence of extensions to fully defined positive Schur multipliers, in terms of operator systems canonically associated with their…

The linear canonical transformations of geometric optics on two-dimensional screens form the group $Sp(4,R)$, whose maximal compact subgroup is the Fourier group $U(2)_F$; this includes isotropic and anisotropic Fourier transforms, screen…

We analyze various consequences in relation to the extension of operators $T:X\to Y$ that are $p$-compact, as well as the extension of operators $T:X\to Y$ whose adjoints $T^*:Y^*\to X^*$ are $p$-compact. In most cases, we discuss these…

We study Toeplitz operators on the Bargmann space, with Toeplitz symbols that are exponentials of complex quadratic forms, from the point of view of Fourier integral operators in the complex domain. Sufficient conditions are established for…

We study composition operators on global classes of ultradifferentiable functions of Beurling type invariant under Fourier transform. In particular, for the classical Gelfand-Shilov classes $\Sigma_d,\ d > 1,$ we prove that a necessary…

A classical theorem of Kuratowski says that every Baire one function on a G_\delta subspace of a Polish (= separable completely metrizable) space X can be extended to a Baire one function on X. Kechris and Louveau introduced a finer…

In the paper, we analyze the Lebesgue exponents $p_\Phi$ and $q_\Phi$, and show that for any $p_\Phi< p < \infty$ and $1< q<q_\Phi$, there exists an equivalent Young function $\Psi$ with $p < p_\Psi < \infty$ and $1<q_\Psi < q$. This type…

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…

Let $\Omega$ be a bounded pseudoconvex domain in $\mathbb{C}^2$ with Lipschitz boundary or a bounded convex domain in $\mathbb{C}^n$ and $\phi\in C(\overline{\Omega})$ such that $H_{\phi}$ is compact on $A^2(\Omega)$. Then $\phi\circ f$ is…

In this work we extend the $L^1$-Bj\"ork-Sj\"olin theory of strongly singular convolution operators to arbitrary graded Lie groups. Our criteria are presented in terms of the oscillating H\"ormander condition due to Bj\"ork and Sj\"olin of…

Let $\Phi$ be a root system of type $A_l$ or $D_l$. Let $K$ be a field of characteristic not $2$. Let $\delta$ be the maximal root of $\Phi$ and set $\Phi_0 = \{\alpha\in\Phi; \delta\perp\alpha\}$. We describe orbits of the group…

We study a family of convolution operators. Their regarding Fourier multipliers are defined in terms of distributions having singularity on the light-cone in $\mathbb{R}^{n+1}$. As a result, we give a new approach to the Bochner-Riesz…

Let $F$ be a local non archimedian field of characteristic $0$, and $G$ a non-connected reductive group over $F$. We denote $G^0$ the connected component of the identity and assume the quotient $G/G^0$ is abelian. For $f$ a locally constant…

Let $X(\mathbb{R})$ be a separable Banach function space such that the Hardy-Littlewood maximal operator is bounded $X(\mathbb{R})$ and on its associate space $X'(\mathbb{R})$. The algebra $C_X(\dot{\mathbb{R}})$ of continuous Fourier…

Let $(\Omega,\mathcal{F},\mathbb{P})$ be a probability space and $\varphi:\ \Omega\times[0,\infty)\to[0,\infty)$ be a Musielak-Orlicz function. In this article, the authors prove that the Doob maximal operator is bounded on the…

Given a $\mathcal{C}^\infty$ expanding map $T$ of the circle, we construct a Hilbert space $\mathcal{H}$ of smooth functions on which the transfer operator $\mathcal{L}$ associated to $T$ acts as a compact operator. This result is made…

In this paper we introduce a new family of operator-valued distributions on Euclidian space acting by convolution on differential forms. It provides a natural generalization of the important Riesz distributions acting on functions, where…

Let $G$ be a locally compact Abelian group with a fixed Haar measure and, denote by $\widehat{G}$ its dual group. In this article, the authors obtain various boundedness of the short-time Fourier transform on Lorentz spaces:…

Let $\Omega$ be a bounded symmetric domain except the two exceptional domains of ${\Bbb C}^N$ and $\phi$ a holomorphic self-map of $\Omega.$ This paper gives a sufficient and necessary condition for the composition operator $C_{\phi}$…

For a locally compact group $G$ we consider the algebra $CD(G)$ of convolution dominated operators on $L^{2}(G)$: An operator $A:L^2(G)\to L^2(G)$ is called convolution dominated if there exists $a\in L^1(G)$ such that for all $f \in…