The Haar System in Besov-type Spaces

2018/08/28 by Wen Yuan, Yuan, Wen, Winfried Sickel +3
Mathematics · #42C15 (Primary) #46E35 (Secondary) #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.1808.09583

openalex publication_date 2018/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Some Besov-type spaces B^s,τ_p,q(ℝⁿ) can be characterized in terms of the behavior of the Fourier--Haar coefficients. In this article, the authors discuss some necessary restrictions for the parameters s, τ, p, q and n of this characterization. Therefore, the authors measure the regularity of the characteristic function \mathcal X of the unit cube in ℝⁿ via the Besov-type spaces B^s,τ_p,q(ℝⁿ). Furthermore, the authors study necessary and sufficient conditions such that the operation ⟨ f, X ⟩ generates a continuous linear functional on B^s,τ_p,q(ℝⁿ).

Citations

• The Q p Carleson measure problem

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