Maciej Rzeszut, Kent State University, Kent, OH, USA: A generalized Johnson Schechtman inequality: Higher order independent sums in product $L^1$ spaces

Description

We generalize the classical theorem of Johnson and Schechtman, We alsonote some interpolation consequences. Let $V^p_{\leq m}\left(\Omega^{\mathbb{N}},B\right)$ be the closed span in $L^p\left(\Omega^{\mathbb{N}},B\right)$ of functions which depend on at most $m$ variables. We express the norm in $V^1_{\leq m}\left(\Omega^{\mathbb{N}}\right)$ in terms of an interpolation sum of mixed $L^1\left(L^2\right)$ norms, which was known for $m=1$ due to Johnson and Schechtman. We also note some consequences concerning interpolation between $ V^1_{\leq m}\left(\Omega^{\mathbb{N}},L^1\right) $ and $ V^1_{\leq m}\left(\Omega^{\mathbb{N}},L^2\right) $, which imply that $ L^1/V^1_{\leq m}\left(\Omega^{\mathbb{N}}\right) $ is of cotype $2$.

Period	08 Jun 2018
Event type	Guest talk
Location	AustriaShow on map