arXiv subjects

Anders Israelsson

Publications and source records attributed to Anders Israelsson.

5 recordsLinked to original sources

arXiv2023

Regularity of oscillatory integral operators

In this paper, we establish the global boundedness of oscillatory integral operators on Besov-Lipschitz and Triebel-Lizorkin spaces, with amplitudes in general $S^m_{ρ,δ}(\mathbb{R}^n)$-classes and non-degenerate phase functions in the class $\textart F^k$. Our results hold for a wide range of parameters $0\leqρ\leq1$, $0\leqδ<1$, $0 0$. We also provide a sufficient condition for the boundedness of operators with amplitudes in the forbidden class $S^m_{1,1}(\mathbb{R}^n)$ in Triebel-Lizorkin spaces.

math.AP↗

arXiv2023

Boundedness of Fourier integral operators on classical function spaces

We investigate the global boundedness of Fourier integral operators with amplitudes in the general Hörmander classes $S^{m}_{ρ, δ}(\mathbb{R}^n)$, $ρ, δ\in [0,1]$ and non-degenerate phase functions of arbitrary rank $κ\in \{0,1,\dots, n-1\}$ on Besov-Lipschitz $B^{s}_{p,q}(\mathbb{R}^n)$ and Triebel-Lizorkin $F^{s}_{p,q}(\mathbb{R}^n)$ of order $s$ and $0<p\leq\infty$, $0<q\leq\infty$. The results that are obtained are all up to the end-point and sharp and are also applied to the regularity of Klein-Gordon-type oscillatory integrals in the aforementioned function spaces.

math.AP↗

arXiv2020

Local and global estimates for hyperbolic equations in Besov-Lipschitz and Triebel-Lizorkin spaces

In this paper we establish optimal local and global Besov-Lipschitz and Triebel-Lizorkin estimates for the solutions to linear hyperbolic partial differential equations. These estimates are based on local and global estimates for Fourier integral operators that span all possible scales (and in particular both Banach and quasi-Banach scales) of Besov-Lipschitz spaces $B^s_{p,q}(\R^n)$, and certain Banach and quasi-Banach scales of Triebel-Lizorkin spaces $F^s_{p,q}(\R^n)$

math.AP↗

arXiv2020

Regularity of Fourier integral operators with amplitudes in general Hörmander classes

We prove the global $L^p$-boundedness of Fourier integral operators that model the parametrices for hyperbolic partial differential equations, with amplitudes in classical Hörmander classes $S^{m}_{ρ, δ}(\mathbb{R}^n)$ for parameters $0<ρ\leq 1$, $0\leq δ<1$. We also consider the regularity of operators with amplitudes in the exotic class $S^{m}_{0, δ}(\mathbb{R}^n)$, $0\leq δ< 1$ and the forbidden class $S^{m}_{ρ, 1}(\mathbb{R}^n)$, $0\leqρ\leq 1.$ Furthermore we show that despite the failure of the $L^2$-boundedness of operators with amplitudes in the forbidden class $S^{0}_{1, 1}(\mathbb{R}^n)$, the operators in question are bounded on Sobolev spaces $H^s(\mathbb{R}^n)$ with $s>0.$ This result extends those of Y. Meyer and E. M. Stein to the setting of Fourier integral operators.

math.AP↗

arXiv2019

Regularity properties of Schrödinger integral operators and general oscillatory integrals

We introduce the notion of Schrödinger integral operators and prove sharp local and global regularity results for these (including propagators for the quantum mechanical harmonic oscillator). Furthermore we introduce general classes of oscillatory integral operators with inhomogeneous phase functions, whose local and global regularity are also established in classical function spaces (both in the Banach and quasi-Banach scales). The results are then applied to obtain optimal (local in time) estimates for the solution to the Cauchy problem for variable-coefficient Schrödinger equations as well as other evolutionary partial differential equations.

math.AP↗