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arXiv · 2505.01573

Boundedness of pseudo-differential operators on the torus revisited. II

Duván Cardona·Manuel Alejandro Martínez
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Abstract

In this paper we continue our program of revisiting the new aspects about the boundedness properties of pseudo-differential operators on the torus. Here we prove $H^p$-$L^p$ and $H^p$-estimates for Hörmander classes of pseudo-differential operators on the torus $\mathbb{T}^n$ for $p\leq 1$. The results are presented in the context of the global symbolic analysis developed by Ruzhansky and Turunen on $\mathbb{T}^n \times \mathbb{Z}^n$ by using the discrete Fourier analysis, which extends the $(ρ, δ)$-Hörmander classes on $\mathbb{T}^n$ defined by local coordinate systems. These results extend those proved by Álvarez and Hounie for the Euclidean case, considering even the case $ρ\leqδ$.

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Duván Cardona, Manuel Alejandro Martínez. 2025-05-02. Boundedness of pseudo-differential operators on the torus revisited. II. https://arxiv.org/abs/2505.01573

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