Variational Formulas of Poincaré-Type Inequalities in Banach Spaces of Functions on the Line

Acta Mathematica Sinica, English Series

Volumn 18, Issue 3, 2002, Pages 417-436

  Chen, Mu Fa ^a  

^a BEIJING NORMAL UNIVERSITY   (China)

Author keywords

Logarithmic Sobolev inequality; Orlicz space; Poincar inequality; Variational formula

Indexed keywords

EID: 0346836853     PISSN: 14398516     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10114-002-0176-8     Document Type: Article

References (20)

1. Chen, M. F.: Variational formulas and approximation theorems for the first eigenvalue in dimension one. Sci. Chin. (A), 44(4), 409-418 (2001)
2. Chen, M. F.: Analytic proof of dual variational formula for the first eigenvalue in dimension one. Sci. Chin. (A), 42(8), 805-815 (1999)
3. Chen, M. F., Wang, F. Y.: Estimation of spectral gap for elliptic operators. Trans. Amer. Math. Soc., 349(3), 1239-1267 (1997)
4. Kantorovich, L. V., Akilov, G. P.: Functional Analysis (2ed), Pergamon Press, Oxford, New York (1982)
5. Bobkov, S. G., Götze, F.: Exponential integrability and transportation cost related to logarithmic Sobolev inequalities. J. Funct. Anal., 163, 1-28 (1999)
6. Mao, Y. H.: The logarithmic Sobolev inequalities for birth-death process and diffusion process on the line. Chin. J. Appl. Prob. Statis., 18(1), 94-100 (2002)
7. Mao, Y. H.: Nash inequalities for Markov processes in dimension one. Acta Math. Sin. Eng. Ser., 18(1), 147-156 (2002)
8. Mao, Y. H.: On empty essential spectrum for Markov processes in dimension one, preprint (2000)
9. Mao, Y. H.: On super-contractivity for Markov semigroups, preprint (2001)
10. Gross, L.: Logarithmic Sobolev inequalities and contractivity of semigroups. LNM., 1563, (1993)
11. Wang, F. Y.: Functional inequalities for empty essential spectrum. J. Funct. Anal., 170, 219-245 (2000)
12. Gong, F. Z., Wang, F. Y.: Functional inequalities for uniformly integrable semigroups and application to essential spectrums. Forum. Math., 14, 293-313 (2002)
13. Muckenhoupt, B.: Hardy's inequality with weights. Studia. Math., (XLIV), 31-38 (1972)
14. Mazya, V. G.: Sobolev Spaces, Springer-Valerg (1985)
15. Opic, B., Kufner, A.: Hardy-type Inequalities, Longman, New York (1990)
16. Chen, M. F.: Explicit bounds of the first eigenvalue. Sci. in China, Ser. A, 43(10), 1051-1059 (2000)
17. Chen, M. F.: Logarithmic Sobolev inequality for symmetric forms. Sci. Chin, 43(6), 601-608 (2000)
18. Wang, F. Y., Sobolev type inequalities for general symmetric forms. Proc. Amer. Math. Soc., 128(12), 3675-3682 (2001)
19. Rao, M. M., Ren, Z. D.: Theory of Orlicz Spaces, Marcel Dekker Inc., New York (1991)
20. Rothaus, O. S.: Analytic inequalities, isoperimetric inequalities and logarithmic Sobolev inequalities. J. Funct. Anal., 64, 296-313 (1985)