6 problems

Endpoint conjecture. Theorem 1.1 should hold under this endpoint assumption: for all $p_1,p_2,p_3\in(1,\infty)$ satisfying $\sum_{i=1}^3p_i^{-1}=1$ and

Let $G$ be a connected Lie group of polynomial growth equipped with a family of left-invariant Hörmander vector fields, let $\Delta_p$ be the associated Laplacian on…

A Banach space $X$ is UMD if its Hilbert transform is bounded on $L^p(\mathbb{R};X)$ for all $p\in(1,\infty)$. It is intermediate UMD if it is $r$-intermediate UMD for some…

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…