Hardy spaces, Besov spaces and Triebel--Lizorkin spaces associated with a discrete Laplacian and applications
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917851391066112 |
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| author | Bui, The Anh Duong, Xuan Thinh |
| author_facet | Bui, The Anh Duong, Xuan Thinh |
| contents | Consider the discrete Laplacian $Δ_d$ defined on the set of integers $\mathbb Z$ by
\[
Δ_d f(n) = -f(n+1) + 2f(n) -f(n-1), \ \ \ \ n\in \mathbb Z,
\]
where $f$ is a function defined on $\mathbb Z$. In this paper, we define Hardy spaces, Besov spaces and Triebel--Lizorkin spaces associated with $Δ_d$ and then show that these function spaces coincide with the classical function spaces defined on $\mathbb Z$. As applications, we prove the boundedness of the spectral multipliers and the Riesz transforms associated with $Δ_d$ on these function spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19399 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hardy spaces, Besov spaces and Triebel--Lizorkin spaces associated with a discrete Laplacian and applications Bui, The Anh Duong, Xuan Thinh Classical Analysis and ODEs 39A12, 35K08, 42A38, 42B35, 42B25, 42B15 Consider the discrete Laplacian $Δ_d$ defined on the set of integers $\mathbb Z$ by \[ Δ_d f(n) = -f(n+1) + 2f(n) -f(n-1), \ \ \ \ n\in \mathbb Z, \] where $f$ is a function defined on $\mathbb Z$. In this paper, we define Hardy spaces, Besov spaces and Triebel--Lizorkin spaces associated with $Δ_d$ and then show that these function spaces coincide with the classical function spaces defined on $\mathbb Z$. As applications, we prove the boundedness of the spectral multipliers and the Riesz transforms associated with $Δ_d$ on these function spaces. |
| title | Hardy spaces, Besov spaces and Triebel--Lizorkin spaces associated with a discrete Laplacian and applications |
| topic | Classical Analysis and ODEs 39A12, 35K08, 42A38, 42B35, 42B25, 42B15 |
| url | https://arxiv.org/abs/2411.19399 |