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On Multiplier Processes Under Weak Moment Assumptions

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Geometric Aspects of Functional Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2169))

Abstract

We show that if \(V \subset \mathbb{R}^{n}\) satisfies a certain symmetry condition that is closely related to unconditionality, and if X is an isotropic random vector for which \(\|\big< X,t\big >\| _{L_{p}} \leq L\sqrt{p}\) for every t ∈ S n−1 and every \(1 \leq p\lesssim \log n\), then the suprema of the corresponding empirical and multiplier processes indexed by V behave as if X were L-subgaussian.

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Acknowledgements

S. Mendelson is supported in part by the Israel Science Foundation.

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Authors and Affiliations

  1. Department of Mathematics, Technion - I.I.T., Haifa, Israel

    Shahar Mendelson

  2. Mathematical Sciences Institute, The Australian National University, Canberra, ACT, Australia

    Shahar Mendelson

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  1. Shahar Mendelson
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Correspondence to Shahar Mendelson .

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Editors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, Tel-Aviv, Israel

    Bo'az Klartag

  2. Mathematics Department, Technion - Israel Institute of Technology, Haifa, Israel

    Emanuel Milman

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Mendelson, S. (2017). On Multiplier Processes Under Weak Moment Assumptions. In: Klartag, B., Milman, E. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2169. Springer, Cham. https://doi.org/10.1007/978-3-319-45282-1_19

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