Related papers: Compact pseudodifferential and Fourier integral op…
The paper contains a survey of a class of Fourier integral operators defined by symbols with tempered weight. These operators are bounded (respectively compact) in $L^2$ if the weight of the amplitude is bounded (respectively tends to $0$).
In some previous papers we have defined and studied a 'magnetic' pseudodifferential calculus as a gauge covariant generalization of the Weyl calculus when a magnetic field is present. In this paper we extend the standard Fourier Integral…
In this paper, we study a class of pseudodifferential operators known as time-frequency localization operators, which depend on a symbol $\varsigma$ and two windows functions $g_1$ and $g_2$. We first present some basic properties of the…
We obtain improved bounds for pseudodifferential operators with rough symbols on Hardy spaces for Fourier integral operators. The symbols $a(x,\eta)$ are elements of $C^{r}_{*}S^{m}_{1,\delta}$ classes that have limited regularity in the…
We carry on the study of Fourier integral operators of H{\"o}rmander's type acting on the spaces $(\mathcal{F}L^p)_{comp}$, $1\leq p\leq\infty$, of compactly supported distributions whose Fourier transform is in $L^p$. We show that the…
We give a criterion for the global boundedness of integral operators which are known to be locally bounded. As an application, we discuss the global $L^p$-boundedness for a class of Fourier integral operators. While the local…
We perform a time-frequency analysis of Fourier multipliers and, more generally, pseudodifferential operators with symbols of Gevrey, analytic and ultra-analytic regularity. As an application we show that Gabor frames, which provide…
Sparsity properties for phase-space representations of several types of operators have been extensively studied in recent papers, including pseudodifferential, Fourier integral and metaplectic operators, with applications to time-frequency…
We introduce the Hardy spaces for Fourier integral operators on Riemannian manifolds with bounded geometry. We then use these spaces to obtain improved local smoothing estimates for Fourier integral operators satisfying the cinematic…
In this paper we investigate the boundedness of sublinear operators generated by fractional integrals as well as sublinear operators generated by Calder\`on-Zygmund operators on generalized weighted Morrey spaces and generalized weighted…
In this article, we explore the boundedness properties of pseudo-differential operators on radial sections of line bundles over the Poincar\'e upper half plane, even when dealing with symbols of limited regularity. We first prove the…
In this work we give H\"older-Besov estimates for periodic Fourier multipliers. We present a class of bounded pseudo-differential operators on periodic Besov spaces with symbols of limited regularity.
The aim of this paper is to get the boundedness of rough sublinear operators generated by fractional integral operators on vanishing generalized weighted Morrey spaces under generic size conditions which are satisfied by most of the…
We obtain a characterization of the weighted inequalities for the Riesz transforms on weighted local Morrey spaces. The condition is sufficient for the boundedness on the same spaces of all Calder\'on-Zygmund operators suitably defined on…
The compactness of the commutators of bilinear fractional integral operators and point-wise multiplication, acting on products of Lebesgue spaces, is characterized in terms of appropriate mean oscillation properties of their symbols. The…
We construct phase space localizing operators in all dimensions. These are frequency localized variants of the conditional expectation operator related to a dyadic stopping time. Our construction is an improvement over the so-called phase…
This paper deals with the problem of when, given a collection $\mathcal C$ of weakly compact operators between separable Banach spaces, there exists a separable reflexive Banach space $Z$ with a Schauder basis so that every element in…
We prove the following localization for compactness of Hankel operators on Bergman spaces. Assume that D is a bounded pseudoconvex domain in C^n, p is a boundary point of D and B(p,r) is a ball centered at p with radius r so that U=D\cap…
We extend the matrix representation of magnetic pseudo-differential operators in a tight Gabor frame from [arXiv:1804.05220, arXiv:2212.12229] to asymmetrical quantizations and smooth symbols dominated by a tempered weight (and not just…
We study weighted composition operators acting between Fock spaces. The following results are obtained: (1) Criteria for the boundedness and compactness; (2) Characterizations of compact differences and essential norm; (3) Complete…