2 problems

Let $(X,\|\cdot\|_X)$ be a $K$-convex Banach space. For $n\in\mathbb{N}$, let $\operatorname{Deg}_{\le d}$ denote the space of functions $f:\{-1,1\}^n\to X$ whose Hamming cube Four…

Let $1<p<\infty$. Let $f\colon\{-1,1\}^{n}\to\mathbb{R}$ satisfy … for every $S\subseteq\{1,\ldots,n\}$ with $|S|<k$, where $P_t$ is the heat semigroup and $L$ is its generator. Me…