arXiv subjects

Albin Petersson

Publications and source records attributed to Albin Petersson.

5 recordsLinked to original sources

arXiv2025

Trace type Orlicz spaces and analysis of Orlicz spaces by Lebesgue exponents

In the paper, we analyze the Lebesgue exponents $p_\Phi$ and $q_\Phi$, and show that for any $p_\Phi< p < \infty$ and $1< q<q_\Phi$, there exists an equivalent Young function $\Psi$ with $p < p_\Psi < \infty$ and $1<q_\Psi < q$. This type of construction is used to improve upon the inclusions $L^{p_\Phi}\cap L^{q_\Phi}\subseteq L^\Phi \subseteq L^{p_\Phi} + L^{q_\Phi}$. For trace type Orlicz spaces $L^{\Phi,\Phi}$, we find that when $\Phi \in \Delta_2$, we have $L^{\Phi,\Phi} \subseteq L^\Phi$ if and only if $\Phi(||f||_{L^\Phi}) \le C \rho_\Phi(f)$ for all $f\in L^\Phi$, and the reverse inclusion is equivalent to the reversed inequality.

math.FA↗

arXiv2025

Fourier Multipliers on Quasi-Banach Orlicz Spaces and Orlicz Modulation Spaces

We find that if a Fourier multiplier is continuous from $L^{\Phi_1}$ to $L^{\Phi_2}$, then it is also continuous from $M^{\Phi_1,\Psi}$ to $M^{\Phi_2,\Psi}$, where $\Phi_1,\Phi_2,\Psi$ are quasi-Young functions and $\Phi_1$ fulfills the $\Delta_2$-condition. This result is applied to show that Mihlin's Fourier multiplier theorem and H\"ormander's improvement hold in certain Orlicz modulation spaces. Lastly, we show that the Fourier multiplier with symbol $m(\xi) = e^{i \mu(\xi)}$, where $\mu$ is homogeneous of order $\alpha$, is bounded on quasi-Banach Orlicz modulation spaces of order $r$, assuming $r\in\big(d/(d+2),1\big]$ and $\alpha\in\big(d(1-r)/r, 2\big]$.

math.FA↗

arXiv2024

Quasi-Banach Schatten-von Neumann properties in Weyl-H\"ormander calculus

We study structural properties of Wiener-Lebesgue spaces with respect to a slowly varying metrics and certain Lebesgue parameters. For $p\in (0,1]$, we deduce Schatten-$p$ properties for pseudo-differential operators whose symbols, together with their derivatives, obey suitable Wiener-Lebesgue-boundedness conditions. Especially, we perform such investigations for the Weyl-H\"ormander calculus. Finally, we apply our results to global-type SG and Shubin pseudo-differential operators.

math.FA↗

arXiv2023

Fourier type operators on Orlicz spaces and the role of Orlicz Lebesgue exponents

We deduce continuity and (global) wave-front properties of classes of Fourier multipliers, pseudo-differential, and Fourier integral operators when acting on Orlicz spaces, or more generally, on Orlicz-Sobolev type spaces. In particular, we extend H{\"o}rmander's improvement of Mihlin's Fourier multiplier theorem to the framework of Orlicz spaces. We also show how Young functions $\Phi$ of the Orlicz spaces are linked to properties of certain Lebesgue exponents $p_\Phi$ and $q_\Phi$ emerged from $\Phi$.

math.FA↗

arXiv2022

Fourier characterizations and non-triviality of Gelfand-Shilov spaces, with applications to Toeplitz operators

We examine properties of Gelfand-Shilov spaces $S_s$, $S^\sigma$, $S^\sigma_s$, $\Sigma_s$, $\Sigma^\sigma$ and $\Sigma^\sigma_s$. These are spaces of smooth functions where the functions or their Fourier transforms admit sub-exponential decay. It is determined that ${\Sigma}^{\sigma}_s$ is nontrivial if and only if $s+ {\sigma} > 1$. We find growth estimates on functions and their Fourier transforms in the one-parameter spaces, and we obtain characterizations in terms of estimates of short-time Fourier transforms for these spaces and their duals. Additionally, we determine conditions on the symbols of Toeplitz operators under which the operators are continuous on one-parameter spaces.

math.FA↗