Related papers: A class of multi-parameter Fourier integral operat…

We study a family of fractional integral operators whose kernels satisfying an non-isotropic dilation have singularity on a coordinate subspace. A characterization is given for these operators bounded from the classical, atom decomposable…

In this paper, we investigate the weighted vector-valued bounds for a class of multilinear singular integral operators, and its commutators, from $L^{p_1}(l^{q_1};\,\mathbb{R}^n,w_1)\times\dots\times L^{p_m}(l^{q_m};\,\mathbb{R}^n,w_m)$ to…

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 first consider two types of localizations of singular integral operators of convolution type, and show, under mild decay and smoothness conditions on the auxiliary functions, that their boundedness on the local Hardy space…

Let $\{K_t\}_{t>0}$ be the semigroup of linear operators generated by a Schr\"odinger operator $-L=\Delta - V(x)$ on $\mathbb R^d$, $d\geq 3$, where $V(x)\geq 0$ satisfies $\Delta^{-1} V\in L^\infty$. We say that an $L^1$-function $f$…

In this paper we study integral operators with kernels \begin{equation*} K(x,y)= k_1( x- A_1y)...k_m( x-A_my), \end{equation*} $k_i(x)=\frac{\Omega_i(x)}{|x|^{n/q_i}}$ where $\Omega_i: \mathbb{R}^n\to \mathbb{R}$ are homogeneous functions…

We consider a class of multiparameter singular Radon integral operators on the Heisenberg group ${\mathbb H}^1$ where the underlying variety is the graph of a polynomial. A remarkable difference with the euclidean case, where Heisenberg…

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 $f\mapsto f\circ\phi$…

By means of a counter-example we show that the multilinear fractional operator is not bounded from a product of Hardy spaces into a Hardy space.

In this article, the authors consider the Schr\"{o}dinger type operator $L:=-{\rm div}(A\nabla)+V$ on $\mathbb{R}^n$ with $n\geq 3$, where the matrix $A$ is symmetric and satisfies uniformly elliptic condition and the nonnegative potential…

Led by the key example of the Korteweg-de Vries equation, we study pairs of Hamiltonian operators which are non-homogeneous and are given by the sum of a first-order operator and an ultralocal structure. We present a complete classification…

Suppose $L=-\Delta+V$ is a Schr\"odinger operator on $\mathbb{R}^n$ with a potential $V$ belonging to certain reverse H\"older class $RH_\sigma$ with $\sigma\geq n/2$. The main aim of this paper is to provide necessary and sufficient…

Given a smooth embedding of manifolds $i: X \hookrightarrow M$ and a Fourier integral operator $\Phi$ acting on $M$, obtained by quantization of a canonical transformation, consider its trace $i^!(\Phi)$ on $X$ (in the sense of relative…

We develop classes of one-parameter families (OPF) of operators on $C^\infty_c(\mathbb{C})$ which characterize the behavior of operators associated to the $\bar\partial$-problem in $L^2(\mathbb{C},e^{-2p})$ where $p$ is a subharmonic,…

In this paper, we give an example of Fourier integral operator with a symbol belongs to $\bigcap\limits_{0<\rho <1}S_{\rho,1}^{0}$ that cannot be extended as a bounded operator on $L^{2}(\mathbb{R}^{n}).$

We prove that a composition operator is bounded on the Hardy space $H^2$ of the right half-plane if and only if the inducing map fixes the point at infinity non-tangentially, and has a finite angular derivative $\lambda$ there. In this case…

We study the boundedness of intrinsic square functions and their commutators on generalized Orlicz-Morrey spaces $M^{\Phi,\varphi}(\mathbb{R}^n)$. In all the cases the conditions for the boundedness are given either in terms of Zygmund-type…

We characterize the semigroups of composition operators that are strongly continuous on the mixed norm spaces $H(p,q,\alpha)$. First, we study the separable spaces $H(p,q,\alpha)$ with $q<\infty,$ that behave as the Hardy and Bergman…

In this paper we prove mixed inequalities for the maximal operator $M_\Phi$, for general Young functions $\Phi$ with certain additional properties, improving and generalizing some previous estimates for the Hardy-Littlewood maximal operator…

This paper investigates the $L^p$ boundedness of wave operators for the Laplace operator with finite rank perturbations \begin{equation*} H=-\Delta+\sum\limits_{i=1}^N\langle\cdot\,, \varphi_i\rangle \varphi_i \qquad \mbox{on}\,\,\, \R^d.…