Special John-Nirenberg-Campanato spaces via congruent cubes

• 作者: Hongchao Jia Jin Tao Dachun Yang Wen Yuan Yangyang Zhang
• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2022,（2）
• 所属期刊栏目: Articles
• 页码范围: 359-420
• 页数: 62页
• 语种: 英文

摘要

Let p ∈[1,∞),q ∈[1,∞),α ∈ R,and s be a non-negative integer.Inspired by the space JNp introduced by John and Nirenberg(1961)and the space B introduced by Bourgain et al.(2015),we introduce a special John-Nirenberg-Campanato space JNcon(p,q,s)αover Rn or a given cube of Rn with finite side length via congruent subcubes,which are of some amalgam features.The limit space of such spaces as p → ∞ is just the Campanato space which coincides with the space BMO(the space of functions with bounded mean oscillations)when α=0.Moreover,a vanishing subspace of this new space is introduced,and its equivalent characterization is established as well,which is a counterpart of the known characterization for the classical space VMO(the space of functions with vanishing mean oscillations)over Rn or a given cube of Rn with finite side length.Furthermore,some VMO-H1-BMO-type results for this new space are also obtained,which are based on the aforementioned vanishing subspaces and the Hardy-type space defined via congruent cubes in this article.The geometrical properties of both the Euclidean space via its dyadic system and congruent cubes play a key role in the proofs of all these results.