Heisenberg群上弱拟正则映射正则性的自我改善  

Self-improving Regularity of Weakly Quasiregular Mappings in Heisenberg Group

作　　者：饶婕晟[1] 郑神州[1] 

机构地区：[1]北京交通大学理学院,北京100044

出　　处：《数学年刊（A辑）》2013年第5期579-588,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11071012)的资助

摘　　要：考虑定义在Heisenberg群上的弱拟正则映射其水平微商可积性的自我改善.在广义水平微商可积指数低于第1层空间维数的情况下,通过接触映射的Jacobian和广义水平微商Jacobian的关系,建立了逆向H(o|¨)lder不等式,从而得到其可积指数的自我提升.In this paper, a self-improving integrability of the horizontal derivatives for weakly quasiregular mappings defined in Heisenberg group is studied. The authors establish a reverse Holder inequality of the horizontal derivatives due to the relationship between Jacobian determinant of contact maps f＊ and the horizontal derivatives H f＊, so that the integrability of horizontal derivatives is shown to have a self-improving effect.

关 键 词：HEISENBERG群 弱拟正则映射 HODGE分解 

分 类 号：O152.1[理学—数学]