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L p-Poincaré inequality for general symmetric forms

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Abstract

L p Poincaré inequalities for general symmetric forms are established by new Cheeger’s isoperimetric constants. L p super-Poincaré inequalities are introduced to describe the equivalent conditions for the L p compact embedding, and the criteria via the new Cheeger’s constants for those inequalities are presented. Finally, the concentration or the volume growth of measures for these inequalities are studied.

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Authors and Affiliations

  1. School of Mathematical Science, LMCS, Ministing of Education, Beijing Normal University, Beijing, 100875, P. R. China

    Yong Hua Mao

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  1. Yong Hua Mao
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Correspondence to Yong Hua Mao.

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Supported in part by Program for New Century Excellent Talents in University (NCET), 973 Project (Grant No. 2006CB805901), National Natural Science Foundation of China (Grant No. 10721091)

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Mao, Y.H. L p-Poincaré inequality for general symmetric forms. Acta. Math. Sin.-English Ser. 25, 2055–2064 (2009). https://doi.org/10.1007/s10114-009-8205-5

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  • DOI: https://doi.org/10.1007/s10114-009-8205-5

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