H型群上的限制性定理和Riesz平均  

Restriction Theorem and Riesz Means on H-type Groups

作　　者：刘和平[1] 王敏 LIU Heping;WANG Min(School of Mathematical Sciences,Peking University,Beijing,100871,P.R.China;School of Science,China University of Geosciences(Beijing),Beijing,100083,P.R.China)

机构地区：[1]北京大学数学科学学院,北京100871 [2]中国地质大学(北京)数理学院,北京100083

出　　处：《数学进展》2025年第2期250-264,共15页Advances in Mathematics(China)

基　　金：国家自然科学基金委青年科学基金(No.12201584)资助。

摘　　要：限制性猜想和Bochner-Riesz猜想是现代调和分析领域尚未完全解决且相互关联的两个重大猜想,相应的问题也是幂零李群上调和分析的重要课题.H型群是特别受到关注的一类两步幂零李群.本文将介绍限制性猜想、Bochner-Riesz猜想在H型群上对应问题的研究进展,以及双线性Riesz平均问题在H型群上的研究成果.The restriction conjecture and the Bochner-Riesz conjecture are two major interrelated conjectures in the field of modern harmonic analysis that remain not fully resolved.The corresponding problems are also significant topics in harmonic analysis on nilpotent Lie groups.H-type groups are a class of two-step nilpotent Lie groups that have garnered particular attention.We introduce the research progress on the problems corresponding to the restriction conjecture and the Bochner-Riesz conjecture on H-type groups,as well as the research findings on the bilinear Riesz means problem on H-type groups.

关 键 词：H型群 限制性定理 RIESZ平均 双线性Riesz平均 

分 类 号：O174.2[理学—数学]