John–Nirenberg–Campanato Spaces. (December 2019) - Tao, Jin; Yang, Dachun; Yuan, Wen
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 → ∞ .