Divergent Fourier series in function spaces near L1- [0;1]

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:505

Article

Kopaliani, Tengiz¹  Samashvili, Nino²  Zviadadze, Shalva¹ 

[1] Javakhishvili Tbilisi State Univ, Fac Exact & Nat Sci, 13 Univ St, Tbilisi 0143, Georgia

[2] Amer Univ Middle East, Coll Engn & Technol, Egaila, Kuwait

关键词: Fourier series;    Uniformly bounded orthonormal system;    Almost everywhere convergence;    Variable exponent Lebesgue space;   

DOI  :  10.1016/j.jmaa.2021.125558

来源: Elsevier

【 摘 要 】

Bochkariev's theorem states that for any uniformly bounded orthonormal system Phi, there is a Lebesgue integrable function such that the Fourier series of it with respect to the system Phi diverges on the set of positive measure. In this paper, we extended Bochkariev's theorem for some class of variable exponent Lebesgue spaces. We characterized the class of variable exponent Lebesgue spaces L-p(.) [0; 1], 1 < p(x) < infinity a.e. on [0;1], such that above mentioned Bochkarev's theorem is valid. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free