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Gaussian 1-Capacity to Gaussian ∞-Capacity

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Gaussian Capacity Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2225))

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Abstract

The development thus far in the previous chapters has not excluded the case p = 1, a situation which almost always requires special treatment involving both analysis and geometry. Our objective in this chapter is to reformulate the Gaussian 1-capacity, characterize the Gaussian Poincaré 1-inequality and Ehrhard’s inequality as well as the Gaussian isoperimetry, and handle the Gaussian ∞-capacity as the dual form of the Gaussian 1-capacity.

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Authors and Affiliations

  1. School of Mathematics, Renmin University of China, Beijing, China

    Liguang Liu

  2. Department Mathematics & Statistics, Memorial University, St. John’s, Newfoundland and Labrador, Canada

    Jie Xiao

  3. Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical Sciences, Beijing Normal University, Beijing, China

    Dachun Yang & Wen Yuan

Authors
  1. Liguang Liu
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  2. Jie Xiao
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  3. Dachun Yang
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  4. Wen Yuan
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Liu, L., Xiao, J., Yang, D., Yuan, W. (2018). Gaussian 1-Capacity to Gaussian ∞-Capacity. In: Gaussian Capacity Analysis. Lecture Notes in Mathematics, vol 2225. Springer, Cham. https://doi.org/10.1007/978-3-319-95040-2_5

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