4 problems

Let $N\in\mathbb{N}$ with $N\geq 2$ and let $0\leq \ell\leq N-2$. For the dyadic collection ${\mathcal E}^N_{\ell,0}$ and the postorder rearrangement operator $\tau_N$, write…

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 a rearrangement of the dyadic intervals, and write $\cF_1,\dots,\cF_N$ for subcollections of the dyadic intervals. Suppose there is a constant $C$ such that, for every…

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…