Related papers: $L^p$-boundedness of multi-parameter Fourier integ…

The local $L^2$-mapping property of Fourier integral operators has been established in H\"ormander \cite{H} and in Eskin \cite{E}. In this paper, we treat the global $L^2$-boundedness for a class of operators that appears naturally in many…

In this paper we study the $L^{p}$-$L^{q}$ boundedness of Fourier multipliers on the fundamental domain of a lattice in $\mathbb{R}^{d}$ for $1 < p,q < \infty$ under the classical H\"ormander condition. First, we introduce Fourier analysis…

Fourier restriction theorems, whose study had been initiated by E.M. Stein, usually describe a family of a priori estimates of the L^q-norm of the restriction of the Fourier transform of a function f in L^p (say, on Euclidean space) to a…

Given a smooth embedding $i\colon X \hookrightarrow M$ of manifolds and a Fourier integral operator $\Phi = \Phi(\Lambda)$ on $M$ associated with a Lagrangian submanifold $\Lambda \subset T^*(X\times X) \setminus \{0\}$, we consider its…

In this paper we study maximal directional singular integral operators in $ \mathbb{R}^n $ given by a H\"ormander--Mihlin multiplier on an $ (n-1)$-dimensional subspace and acting trivially in the perpendicular direction. The subspace is…

In this paper we consider the wave operators $W_{\pm}$ for a Schr\"odinger operator $H$ in ${\bf{R}}^n$ with $n\geq 4$ even and we discuss the $L^p$ boundedness of $W_{\pm}$ assuming a suitable decay at infinity of the potential $V$. The…

We study the Hp-Lq boundedness of certain integral operators of fractional type.

We consider the fourth order Schr\"odinger operator $H=\Delta^2+V(x)$ in three dimensions with real-valued potential $V$. Let $H_0=\Delta^2$, if $V$ decays sufficiently and there are no eigenvalues or resonances in the absolutely continuous…

The purpose of this paper is to study the $L^p$ boundedness of operators of the form \[ f\mapsto \psi(x) \int f(\gamma_t(x))K(t)\: dt, \] where $\gamma_t(x)$ is a $C^\infty$ function defined on a neighborhood of the origin in $(t,x)\in…

We prove that the low energy parts of the wave operators $W_\pm$ for Schr\"odinger operators $H = -\lap + V(x)$ on $\R^4$ are bounded in $ L^p(\R^4)$ for $1<p\leq 2$ and are unbounded for $2<p\leq \infty$ if $H$ has resonances at the…

This paper is devoted to conducting a comprehensive and self-contained study of the boundedness on modulation spaces of Fourier integral operators arising when solving Schr\"{o}dinger type operators. The symbols of these operators belong to…

We investigate two types of boundedness criteria for bilinear Fourier multiplier operators with symbols with bounded partial derivatives of all (or sufficiently many) orders. Theorems of the first type explicitly prescribe only a certain…

We study a class of Fourier integral operators on compact manifolds with boundary, associated with a natural class of symplectomorphisms, namely, those which preserve the boundary. A calculus of Boutet de Monvel's type can be defined for…

In this article, we study properties of multilinear Fourier integral operators on weighted modulation spaces. In particular, using the theory of Gabor frames, we study boundedness of multilinear Fourier integral operators on products of…

We study the boundedness of commutators of bi-parameter singular integrals between mixed spaces $$ [b,T]: L^{p_1}L^{p_2} \to L^{q_1}L^{q_2} $$ in the off-diagonal situation $q_i,p_i\in(1,\infty)$ where we also allow $q_i\not= p_i.$…

Let H(f)(x)=\int_{(0,infty)^d} f(v) E_{x}(v) d\nu(v), be the multivariable Hankel transform, where E_{x}(v)=\prod_{k=1}^d (x_k v_k)^{-a_k+1/2} J_{a_k-1/2}(x_k v_k), d\nu(v)=v^a dv, a=(a_1,...,a_d). We give sufficient conditions on a bounded…

Let $m(\xi,\eta)$ be a measurable locally bounded function defined in $\mathbb R^2$. Let $1\leq p_1,q_1,p_2,q_2<\infty $ such that $p_i=1$ implies $q_i=\infty $. Let also $0<p_3,q_3<\infty $ and $1/p=1/p_1+1/p_2-1/p_3$. We prove the…

In this work, we provide a complete characterization of the boundedness of two classes of multiparameter Forelli-Rudin type operators from one mixed-norm Lebesgue space $L^{\vec p}$ to another space $L^{\vec q}$, when $1\leq \vec{p}\leq…

In this paper we investigate the $L^p$-boundedness of certain classes of periodic pseudo-differential operators. The operators considered arise from the study of symbols on $\mathbb{T}^n\times\mathbb{Z}^n$ with limited regularity.

The notion of invariant operators, or Fourier multipliers, is discussed for densely defined operators on Hilbert spaces, with respect to a fixed partition of the space into a direct sum of finite dimensional subspaces. As a consequence,…