Related papers: Continuity of composition operators in Sobolev spa…

In this paper we consider composition operators on locally convex spaces of functions defined on $\mathbb{R}$. We prove results concerning supercyclicity, power boundedness, mean ergodicity and convergence of the iterates in the strong…

We prove lifting theorems for complex representations $V$ of finite groups $G$. Let $\sigma=(\sigma_1,\dots,\sigma_n)$ be a minimal system of homogeneous basic invariants and let $d$ be their maximal degree. We prove that any continuous map…

We introduce $p$-adic Kummer spaces of continuous functions on $\mathbb{Z}_p$ that satisfy certain Kummer type congruences. We will classify these spaces and show their properties, for instance, ring properties and certain decompositions.…

The Invariant Subspace Problem ("ISP") for Hilbert space operators is known to be equivalent to a question that, on its surface, seems surprisingly concrete: For composition operators induced on the Hardy space H^2 by hyperbolic…

In this paper we study the embedding problem of an operator into a strongly continuous semigroup. We obtain characterizations for some classes of operators, namely composition operators and analytic Toeplitz operators on the Hardy space…

For $1 < p < \infty$ let $\mathcal{T}_p ^\alpha$ be the norm closure of the algebra generated by Toeplitz operators with bounded symbols acting on the standard weighted Fock space $F_\alpha ^p$. In this paper, we will show that an operator…

In this paper we establish global Lp regularity properties of Fourier integral operators. The orders of decay of the amplitude are determined for operators to be bounded on $L^p(\Rn)$, $1<p<\infty$, as well as to be bounded from Hardy space…

We develop the compactness theory of multilinear singular integrals on product spaces using a modern point of view. The first main result is a compact $T1$ theorem for multilinear Calder\'{o}n--Zygmund operators on product spaces. More…

Recently, it was shown that the image of a Toeplitz kernel of dimension greater than $1$ under composition by an inner function is nearly $S^*$-invariant if and only if the inner function is an automorphism. Building on this, we determine…

We study composition operators on the Schwartz space of rapidly decreasing functions. We prove that such a composition operator is never a compact operator and we obtain necessary or sufficient conditions for the range of the composition…

Let $L^m_p(R^n)$, $p\in [1,\infty]$, be the homogeneous Sobolev space, and let $E\subset R^n$ be a closed set. For each $p>n$ and each non-negative integer $m$ we give an intrinsic characterization of the restrictions to $E$ of $m$-jets…

Let $\Omega_1,\Omega_2\subset {\mathbb C}$ be bounded domains. Let $\phi:\Omega_1\rightarrow \Omega_2$ holomorphic in $\Omega_1$ and belonging to $W^{1,\infty}_{\Omega_2}(\Omega_1)$. We study the composition operators $f\mapsto f\circ\phi$…

The paper contains a brief description of a simplified version of A. Sobolev's proof of absolute continuity of spectra of periodic magnetic Schr\"{o}dinger operators. This approach is applicable to all periodic elliptic operators known to…

Let a:[0,1] -> R be a Lebesgue-almost everywhere positive function. We consider the Riemann-Liouville operator R^a of variable order a(.) as an operator from L_p[0,1] to L_q[0,1]. Our first aim is to study its continuity properties. For…

We study the mapping properties of fractional maximal operators in Sobolev and Campanato spaces in metric measure spaces. We show that, under certain restrictions on the underlying metric measure space, fractional maximal operators improve…

We construct explicit examples of Frostman-type measures concentrated on arbitrary planar rectifiable curves of positive length. Based on such constructions we obtain for each $p \in (1,\infty)$ an exact description of the trace space of…

A representation of the $\mathfrak{so}(2,5)$ algebra corresponding to the continuous spin field in $\mathbf{AdS_6}$ is considered. The algebra is realized using the Lie-Lorentz derivative, which naturally incorporates $\mathbf{AdS_6}$…

We study composition operators between weighted Bergman spaces of the polydisc induced by smooth symbols. We prove a general result of continuity which only involves the behaviour of the symbol on the polytorus. We deduce from this several…

For $0 < s < 1 < q < \infty$, we characterize the homeomorphisms $\varphi : \real^n \to \real^n$ for which the composition operator $f \mapsto f \circ \varphi$ is bounded on the homogeneous, scaling invariant Besov space…

Fix strictly increasing right continuous functions with left limits $W_i:\bb R \to \bb R$, $i=1,...,d$, and let $W(x) = \sum_{i=1}^d W_i(x_i)$ for $x\in\bb R^d$. We construct the $W$-Sobolev spaces, which consist of functions $f$ having…