JOHN-NIRENBERG-Q SPACES VIA CONGRUENT CUBES  

作　　者：陶金 杨珍瑜 袁文 Jin TAO;Zhenyu YANG;Wen YUAN(Laboratory of Mathematics and Complex Systems(Ministry of Education of China),School of Mathematical Sciences,Beijing Normal University,Beijing 100875,China)

机构地区：[1]Laboratory of Mathematics and Complex Systems(Ministry of Education of China),School of Mathematical Sciences,Beijing Normal University,Beijing 100875,China

出　　处：《Acta Mathematica Scientia》2023年第2期686-718,共33页数学物理学报（B辑英文版）

基　　金：partially supported by the National Natural Science Foundation of China(12122102 and 11871100);the National Key Research and Development Program of China(2020YFA0712900)。

摘　　要：To shed some light on the John-Nirenberg space,the authors of this article introduce the John-Nirenberg-Q space via congruent cubes,JNQp,qα(Rn),which,when p=∞and q=2,coincides with the space Qα(Rn)introduced by Essen,Janson,Peng and Xiao in[Indiana Univ Math J,2000,49(2):575-615].Moreover,the authors show that,for some particular indices,JNQp,qα(Rn)coincides with the congruent John-Nirenberg space,or that the(fractional)Sobolev space is continuously embedded into JNQp,qα(Rn).Furthermore,the authors characterize JNQp,qα(Rn)via mean oscillations,and then use this characterization to study the dyadic counterparts.Also,the authors obtain some properties of composition operators on such spaces.The main novelties of this article are twofold:establishing a general equivalence principle for a kind of’almost increasing’set function that is here introduced,and using the fine geometrical properties of dyadic cubes to properly classify any collection of cubes with pairwise disjoint interiors and equal edge length.

关 键 词：John-Nirenberg space congruent cube Q space (fractional)Sobolev space mean oscillation dyadic cube composition operator 

分 类 号：O177[理学—数学]