HEISENBERG_GROUP

作品数：77被引量：88H指数：5
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相关机构：浙江大学南京理工大学南京林业大学更多>>
相关期刊：《Journal of Partial Differential Equations》《Progress in Natural Science:Materials International》《Analysis in Theory and Applications》《Frontiers of Mathematics in China》更多>>
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The tangential k-Cauchy-Fueter type operator and Penrose type integral formula on the generalized complex Heisenberg group
《Applied Mathematics(A Journal of Chinese Universities)》2024年第1期181-190,共10页REN Guang-zhen SHI Yun KANG Qian-qian 
Supported by National Nature Science Foundation in China(12101564,11971425,11801508);Nature Science Foundation of Zhejiang province(LY22A010013);Domestic Visiting Scholar Teacher Professional Development Project(FX2021042)。
The tangential k-Cauchy-Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables,respectively.I...
关键词：the generalized complex Heisenberg group the tangential k-Cauchy-Fueter type operator Penrose-type integral formula 
On fundamental solution for powers of the sub-Laplacian on the Heisenberg group被引量：1
《Applied Mathematics(A Journal of Chinese Universities)》2017年第3期365-378,共14页WANG Hai-meng WU Qing-yan 
Supported by Doctor Special Foundation of Jiangsu Second Normal University(JSNU2015BZ07)
We discuss the fundamental solution for m-th powers of the sub-Laplacian on the Heisenberg group. We use the representation theory of the Heisenberg group to analyze the associated m-th powers of the sub-Laplacian and...
关键词：SUB-LAPLACIAN fundamental solution group Fourier transform Plancherel formula Heisenberg group 
Characterizations of Sobolev spaces in Euclidean spaces and Heisenberg groups被引量：3
《Applied Mathematics(A Journal of Chinese Universities)》2013年第4期531-547,共17页CUI Xiao-yue LAM Nguyen LU Guo-zhen 
supported by a US NSF grant DMS-1301595
Recently, many new features of Sobolev spaces W k,p ？RN ？ were studied in [4-6, 32]. This paper is devoted to giving a brief review of some known characterizations of Sobolev spaces in Euclidean spaces and describin...
关键词：characterization of Sobelev spaces Folland-Stein space Poincar′e inequalities Heisenberg group second order Sobolev space 
A restriction theorem for the quaternion Heisenberg group被引量：1
《Applied Mathematics(A Journal of Chinese Universities)》2011年第1期86-92,共7页LIU He-ping WANG Ying-zhan 
Supported by National Natural Science Foundation of China (10871003, 10990012);the Specialized Research Fund for the Doctoral Program of Higher Education of China (2007001040)
We prove that the restriction operator for the sublaplacian on the quaternion Heisenberg group is bounded from L^p to L^p＇ if 1 ≤ p ≤4/3. This is different from the Heisenberg group, on which the restriction operat...
关键词：Quaternion Heisenberg group restriction operator special Hermite expansion. 
Some embedding theorems for W～(1,p)(Ω, H～n)
《Applied Mathematics(A Journal of Chinese Universities)》2010年第1期85-92,共8页JIA Gao ZHANG Guo-qing 
Supported by Shanghai Leading Academic Discipline Project (S30501);Innovation Programm of Shanghai Municipal Education Commission (08YZ94)
For the maps on the Heisenberg group target, we prove a Poincare type inequality. Applying this Poincare type inequality, we obtain the corresponding versions of Sobolev and Rellich embedding theorems.
关键词：Heisenberg group HSlder continuity embedding theorem. 
Mean size formula of wavelet subdivision tree on Heisenberg group
《Applied Mathematics(A Journal of Chinese Universities)》2008年第3期303-312,共10页WANG Guo-mao Department of Mathematics,Zhejiang University,Hangzhou 310027,China Department of Mathematics,Hangzhou Dianzi University,Hangzhou 310018,China. 
the National Natural Science Foundation of China (10471123; 10771190)
The purpose of this paper is to investigate the mean size formula of wavelet packets （wavelet subdivision tree） on Heisenberg group. The formula is given in terms of the p-norm joint spectral radius. The vector refi...
关键词：Heisenberg group wavelet packets subdivision tree joint spectral radius STABILITY 
SOME NEW PROPERTIES ON L^p(Ω,H^n)被引量：1
《Applied Mathematics(A Journal of Chinese Universities)》2007年第2期174-180,共7页Jia Gao 
Supported by the NNSF of China(10471063);the EF of Shanghai(06EZ033).
Let L^p（Ω, H^n） indicate the L^P-space of the maps for Heisenberg group target. In this paper some new properties are obtained for the space L^p（Ω, H^n）
关键词：Heisenberg group L^P-space quasi-center of mass 
LOWER SEMICONTINUITY OF A CLASS OF FUNCTIONALSIN SBV_H
《Applied Mathematics(A Journal of Chinese Universities)》2005年第1期27-34,共8页SongYingqing YangXiaoping LongFei 
In this paper lower semicontinuity of the functional I(u)=∫_Ωf(x,u,Δ~ _Hu)dx is investigated for f being a Carathéodory function defined on Hn×R×R^2n and for u∈SBV_H(Ω),where Hn is the Heisenberg group with di...
关键词：lower semicontinuity SBV_H function Heisenberg group Lusin approximation. 
SOLVABILITY OF THE FOURTH ORDER NONLINEAR SUBELLIPTIC EQUATIONS ON THE HEISENBERG GROUP
《Applied Mathematics(A Journal of Chinese Universities)》2003年第1期45-52,共8页Zhang JihuiSchool of Math.& Computer Science,Nanjing Normal Univ.,Nanjing 210097,China. Tianshui Teachers College, Tianshui 741000,China. 
theNationalNaturalScienceFoundationofChina (199710 68)andtheNSFofEducationCommitteeofJiangsuProvince .
In this paper,some existence results for the fourth order nonlinear subelliptic equations on the Heisenberg group are given by means of variational methods.
关键词：Heisenberg group nonlinear problem subelliptic equation variational method existence vector. 
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