Estimates for pseudo-differential operators on the torus revisited. I
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| Format: | Preprint |
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2025
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| _version_ | 1866915449963282432 |
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| author | Cardona, Duván Martínez, Manuel Alejandro |
| author_facet | Cardona, Duván Martínez, Manuel Alejandro |
| contents | In this paper we prove $L^p$-estimates for Hörmander classes of pseudo-differential operators on the torus $\mathbb{T}^n$. The results are presented in the context of the global symbolic calculus of Ruzhansky and Turunen on $\mathbb{T}^n\times\mathbb{Z}^n$ by using the discrete Fourier analysis on the torus which extends the usual ($ρ,δ$)-Hörmander classes on $\mathbb{T}^n$. The main results extend Álvarez and Hounie's method for $\mathbb{R}^n$ to the torus, and Fefferman's $L^p$-boundedness theorem in the toroidal setting allowing the condition $δ\geqρ$. When $δ\leq ρ$, our results recover the available estimates in the literature. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_20575 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Estimates for pseudo-differential operators on the torus revisited. I Cardona, Duván Martínez, Manuel Alejandro Analysis of PDEs Functional Analysis In this paper we prove $L^p$-estimates for Hörmander classes of pseudo-differential operators on the torus $\mathbb{T}^n$. The results are presented in the context of the global symbolic calculus of Ruzhansky and Turunen on $\mathbb{T}^n\times\mathbb{Z}^n$ by using the discrete Fourier analysis on the torus which extends the usual ($ρ,δ$)-Hörmander classes on $\mathbb{T}^n$. The main results extend Álvarez and Hounie's method for $\mathbb{R}^n$ to the torus, and Fefferman's $L^p$-boundedness theorem in the toroidal setting allowing the condition $δ\geqρ$. When $δ\leq ρ$, our results recover the available estimates in the literature. |
| title | Estimates for pseudo-differential operators on the torus revisited. I |
| topic | Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2502.20575 |