논문KCI 등재
A HARDY INEQUALITY ON H-TYPE GROUPS
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
We prove a Hardy inequality related to Carnot-Carath´eodory distance on H-type groups based on a representation formula on such groups.
Abstract
We prove a Hardy inequality related to Carnot-Carath´eodory distance on H-type groups based on a representation formula on such groups.
참고문헌 (22)
- R. Beals, "Hamilton-Jacobi theory and the heat kernel on Heisenberg groups", J. Math. Pures Appl. (9), 79(7), pp.633~689 (2000)
- A. Bonfiglioli, "Nonlinear Liouville theorems for some critical problems on H-type groups", J. Funct. Anal, 207(1), pp.161~215 (2004)
- W. Cohn, "Best constants for Moser-Trudinger inequalities on the Heisenberg group", Indiana Univ. Math. J, 50(4), pp.1567~1591 (2001)
- W. Cohn, "Best constants for Moser-Trudinger inequalities, fundamental solutions and one-parameter representation formulas on groups of Heisenberg type", Acta Math. Sin. (Engl. Ser.), 18(2), pp.375~390 (2002)
- L. D’Ambrosio, "Some Hardy inequalities on the Heisenberg group", Differ. Equ, 40(4), pp.552~564 (2004)
- L. D’Ambrosio, "Hardy inequalities related to Grushin type operators", Proc. Amer. Math. Soc, 132(3), pp.725~734 (2004)
- L. D’Ambrosio, "Hardy-type inequalities related to degenerate elliptic differential operators", Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 4(3), pp.451~486 (2005)
- D. Danielli, "Hardy-Sobolev type inequalities with sharp constants in Carnot-Carath´eodory spaces", Potential Anal, 34(3), pp.223~242 (2011)
- N. Eldredge, "Precise estimates for the subelliptic heat kernel on H-type groups", J. Math. Pures Appl., 92(1), pp.52~85 (2009)
- N. Garofalo, "Frequency functions on the Heisenberg group, the uncer- tainty principle and unique continuation", Ann. Inst. Fourier, 40(2), pp.313~356 (1990)
- J. A. Goldsteinand, "On a degenerate heat equation with a singular potential", J. Funct. Anal, 186(2), pp.342~359 (2001)
- J.-Q. Hu, "Gradient estimates for the heat semigroup on H-type groups", Potential Anal, 33(4), pp.355~386 (2010)
- H. Hueber, "Asymptotics for some Green kernels on the Heisenberg group and the Martin boundary", Math. Ann, 283(1), pp.97~119 (1989)
- A. Kaplan, "Fundamental solution for a class of hypoelliptic PDE generated by compo- sition of quadratic forms", Trans. Amer. Math. Soc, 258(1), pp.147~153 (1980)
- H.-Q. Li, "Estimation optimale du gradient du semi-groupe de la chaleur sur le groupe de Heisenberg", J. Funct. Anal, 236(2), pp.369~394 (2006)
- H.-Q. Li, "Estimations asymptotiques du noyau de la chaleur sur les groupes de", C. R. Math. Acad. Sci. Paris, 344(8), pp.497~502 (2007)
- H.-Q. Li, "Estimations optimales du noyau de la chaleur sur les groupes de type Heisen- berg", J. Reine Angew. Math, 646, pp.195~233 (2010)
- H.-Q. Li, "Fonctions maximales centr´ees de Hardy-Littlewood sur les groupes de Heisen- berg", Studia Math, 191(1), pp.89~100 (2009)
- R. Monti, "Some properties of Carnot-Carath´eodory balls in the Heisenberg group", Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl, 11(3), pp.155~167 (2000)
- R. Monti, "Surface measures in Carnot-Carath´eodory spaces", Calc. Var. Partial Differential Equations, 13(3), pp.339~376 (2001)
- P. Niu, "Hardy type and Rellich type inequalities on the Heisen- berg group", Proc. Amer. Math. Soc, 129(12), pp.3623~3630 (2001)
- L. Zhu, "A Hardy inequality for the Grushin type operators", Math. Inequal Appl, 12(4), pp.923~930 (2012)
관련 논문AI추천
Hardy inequalities in half spaces of the Heisenberg groupJunqiang Han, Pengcheng Niu, Wenji Qin대한수학회 · 대한수학회보2008 · 제45권 제3호Estimates for the Riesz transforms associated with Schr\"odinger type operators on the Heisenberg groupYanhui Wang대한수학회 · 대한수학회보2022 · 제59권 제5호Lp ESTIMATES FOR SCHR¨ODINGER TYPE OPERATORS ON THE HEISENBERG GROUPLiu Yu대한수학회 · 대한수학회지2010 · 제47권 제2호Hardy type estimates for Riesz transforms associated with Schr\"{o}dinger operators on the Heisenberg groupChunfang Gao대한수학회 · 대한수학회지2022 · 제59권 제2호A Neumann type problem on an unbounded domain in the Heisenberg groupAshutosh Pandey, Mukund Madhav Mishra, Shivani Dubey대한수학회 · 대한수학회지2022 · 제59권 제3호FRACTIONAL INTEGRAL ALONG HOMOGENEOUS CURVES IN THE HEISENBERG GROUP김준일대한수학회 · 대한수학회지2005 · 제42권 제3호
이 간행물의 다른 논문 (18건)
CONSTANT-SIGN SOLUTIONS OF p-LAPLACIAN TYPE OPERATORS ON TIME SCALES VIA VARIATIONAL METHODSWeigao Ge, Li Zhangpp. 1131-1145COINCIDENCE THEOREMS FOR NONCOMPACT RC-MAPS IN ABSTRACT CONVEX SPACES WITH APPLICATIONSMing-ge Yang, Nan-Jing Huangpp. 1147-1161EINSTEIN HALF LIGHTLIKE SUBMANIFOLDS WITH SPECIAL CONFORMALITIES진대호, 송대진pp. 1163-1178DOUBLY NONLINEAR PARABOLIC EQUATIONS INVOLVING p-LAPLACIAN OPERATORS VIA TIME-DISCRETIZATION METHODSujin Kang, 신기연pp. 1179-1192GLOBAL STABILITY ANALYSIS FOR A CLASS OF COHEN-GROSSBERG NEURAL NETWORK MODELSYingxin Guopp. 1193-1198
