Timeline for Bound for a conditional expectation

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Aug 15, 2018 at 12:01	comment	added	Iosif Pinelis		Haagerup mainly avoided the terminology of random variables (r.v.'s). In particular, instead of Rademacher r.v.'s, he used Rademacher functions. He apparently did not explicitly used normal r.v.'s. However, the two kinds of terminology, the analytical and probabilistic ones, are easily translatable into each other. In particular, it is not hard to see that the constant $B_p$ for $p\ge2$ in Haagerup's paper equals $(\mathsf{E}\,\|Z\|^p)^{1/p}$, where $Z\sim N(0,1)$.
Aug 15, 2018 at 1:20	comment	added	user124297		Haagerup inequality is for the Rademacher r.v., can you please elaborate how you get normal vector on the right hand side. Thank you.
Jun 6, 2018 at 0:26	comment	added	Iosif Pinelis		@user124297 : If the setting is different from the one described in my answer, then the argument will not hold without adjustment.
Jun 5, 2018 at 19:39	comment	added	user124297		Thank you for your answer. I have gotten curious now- if $r_i$ and $\varepsilon_i$ are not dependent. Say, we would like to bound $\sum_{I=1}^na_ir_i$, under condition on $r_i$. Would the same procedure work? Thank you.
Jun 4, 2018 at 2:30	vote	accept	user124297
Jun 4, 2018 at 2:20	history	edited	Iosif Pinelis	CC BY-SA 4.0	added 2 characters in body
Jun 4, 2018 at 2:15	history	answered	Iosif Pinelis	CC BY-SA 4.0