arXiv Open Access 2024

Hardy spaces, Besov spaces and Triebel--Lizorkin spaces associated with a discrete Laplacian and applications

The Anh Bui Xuan Thinh Duong

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Abstrak

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.

Topik & Kata Kunci

math.CA

Penulis (2)

The Anh Bui

Xuan Thinh Duong

Format Sitasi

APA MLA BibTeX

Bui, T.A., Duong, X.T. (2024). Hardy spaces, Besov spaces and Triebel--Lizorkin spaces associated with a discrete Laplacian and applications. https://arxiv.org/abs/2411.19399

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Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓