John–Nirenberg–Campanato Spaces. (December 2019)

• Record Type: Journal Article
• Authors: Tao, Jin; Yang, Dachun; Yuan, Wen
• Is Part Of: Nonlinear analysis. Volume 189(2019)
• Publication Date: 2019-12
• Subjects: primary 42B35 -- secondary 42B30 46E35; Cube -- Euclidean space -- John–Nirenberg–Campanato space -- John–Nirenberg inequality -- Polymer -- Duality; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111584
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Let p ∈ ( 1, ∞ ), q ∈ [ 1, ∞ ), α ∈ [ 0, ∞ ) and s be a non-negative integer. In this article, the authors introduce the John–Nirenberg–Campanato space J N ( p, q, s ) α ( X ), where X is R n or any cube Q 0 ⫋ R n, which when α = 0 and s = 0 coincides with the J N p -space introduced by F. John and L. Nirenberg in the sense of equivalent norms. The authors then give the predual space of J N ( p, q, s ) α ( X ) and a John–Nirenberg type inequality of John–Nirenberg–Campanato spaces. Moreover, the authors prove that the classical Campanato space serves as a limit space of J N ( p, q, s ) α ( X ) when p → ∞ .