3 problems

Let $X$ be an $r$-intermediate UMD space for some $r\in(2,\infty)$. Equivalently, there exist a UMD space $Y$ and a Hilbert space $H$ forming a compatible couple such that $X$ is i…

Let $M=\{m_j:j\geq1\}$ be a shift, and set $N_j(M)$ for the associated Semenov counting quantity. A sequence is called decomposable when it satisfies the hypothesis of Definition 1…

Let $T$ be the scalar-valued rearrangement operator associated with a rearrangement of the dyadic Haar system, and let $L^p_E$ denote the Bochner space of $E$-valued functions. Ass…