Related papers: Compact pseudodifferential and Fourier integral op…
Cut vertices, a generalization of matrix elements of local operators, are revisited, and an expansion in terms of minimally subtracted cut vertices is formulated. An extension of the formalism to deal with semi-inclusive deep inelastic…
We consider a class of Fourier integral operators, globally defined on $\mathbb{R}^{d}$, with symbols and phases satisfying product type estimates (the so-called $SG$ or scattering classes). We prove a sharp continuity result for such…
In this work we show endpoint boundedness properties of pseudo-differential operators of type $(\rho,\rho)$, $0<\rho<1$, on Triebel-Lizorkin and Besov spaces. Our results are sharp and they also cover operators defined by compound symbols.
Let $X$ be a compact manifold with boundary. Suppose that the boundary is fibred, $\phi:\pa X\longrightarrow Y,$ and let $x\in\CI(X)$ be a boundary defining function. This data fixes the space of `fibred cusp' vector fields, consisting of…
We formulate the issue of minimality of self-adjoint operators on a Hilbert space as a semi-definite problem, linking the work by Overton in [1] to the characterization of minimal hermitian matrices. This motivates us to investigate the…
We mostly survey results concerning the $L^2$ boundedness of oscillatory and Fourier integral operators. This article does not intend to give a broad overview; it mainly focusses on a few topics directly related to the work of the authors.
We obtain a complete characterization of the entire functions $g$ such that the integral operator $(T_ g f)(z)=\int_{0}^{z}f(\zeta)\,g'(\zeta)\,d\zeta$ is bounded or compact, on a large class of Fock spaces $\mathcal{F}^\phi_p$, induced by…
We study the global boundedness of bilinear and multilinear Fourier integral operators on Banach and quasi-Banach $L^p$ spaces, where the amplitudes of the operators are smooth or rough in the spatial variables. The results are obtained by…
The relationship between the operator approximation property and the strong operator approximation property has deep significance in the theory of operator algebras. The original definitions of Effros and Ruan, unlike the classical…
In this paper, we give several characterizations for the boundedness of multilinear Rihaczek distributions acting from Wiener amalgam spaces to modulation and Fourier modulation spaces. Moreover, we establish the crucial self-improvement…
Related to a semigroup of operators on a metric measure space, we define and study pseudodifferential operators (including the setting of Riemannian manifold, fractals, graphs ...). Boundedness on $L^p$ for pseudodifferential operators of…
This article addresses linear hyperbolic partial differential equations and pseudodifferential equations with strongly singular coefficients and data, modelled as members of algebras of generalised functions. We employ the recently…
We introduce an operator valued Short-Time Fourier Transform for certain classes of operators with operator windows, and show that the transform acts in an analogous way to the Short-Time Fourier Transform for functions, in particular…
The aim of this paper is to investigate the boundedness of periodic Fourier integral operators in Lebesgue spaces with variable exponent $L^{p(\cdot)}$ on the $n$-dimensional torus. We deal with operators of type $(\rho, \delta)$ which…
Fractional difference sequence spaces have been studied in the literature recently. In this work, some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain operators on some difference…
First, we reconsider the magnetic pseudodifferential calculus and show that for a large class of non-decaying symbols, their corresponding magnetic pseudodifferential operators can be represented, up to a global gauge transform, as…
We introduce new quasi-Banach modulation spaces on locally compact abelian (LCA) groups which coincide with the classical ones in the Banach setting and prove their main properties. Then we study Gabor frames on quasi-lattices,…
We reduce the boundedness of operators in Morrey spaces $L_p^r({\mathbb R}^n)$, its preduals, $H^{\varrho}L_p ({\mathbb R}^n)$, and their preduals $\overset{\circ}{L}{}^r_p({\mathbb R}^n)$ to the boundedness of the appropriate operators in…
In this paper, the authors define the mixed $\lambda$-central Morrey spaces and the mixed $\lambda$-central $BMO$ spaces. The boundedness of the fractional integral operators $T_{\alpha}$ and its commutators $[b, T_{\alpha}]$ are…
Recent decades have provided a host of examples and applications motivating the study of nonlocal differential operators. We discuss a class of such operators acting on bounded domains, focusing on those with integrable kernels having…