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Hanson-Wright inequality in Banach spaces
Radosław Adamczak, Rafał Latała, Rafał Meller · 2018-11-01 · via math.ST updates on arXiv.org

We discuss two-sided bounds for moments and tails of quadratic forms in Gaussian random variables with values in Banach spaces. We state a natural conjecture and show that it holds up to additional logarithmic factors. Moreover in a certain class of Banach spaces (including $L_r$-spaces) these logarithmic factors may be eliminated. As a corollary we derive upper bounds for tails and moments of quadratic forms in subgaussian random variables, which extend the Hanson-Wright inequality.

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