Boundedness of pseudo-differential operators on the torus revisited. II
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908347080376320 |
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| author | Cardona, Duván Martínez, Manuel Alejandro |
| author_facet | Cardona, Duván Martínez, Manuel Alejandro |
| contents | 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 $ρ\leqδ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01573 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundedness of pseudo-differential operators on the torus revisited. II Cardona, Duván Martínez, Manuel Alejandro Analysis of PDEs Functional Analysis 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 $ρ\leqδ$. |
| title | Boundedness of pseudo-differential operators on the torus revisited. II |
| topic | Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2505.01573 |