Dimension dependence of factorization problems: Hardy spaces and $S{L}_n^{\infty }$

Abstract

Given $1\le p<\infty$, let $W_n$ denote the finite-dimensional dyadic Hardy space $H_n^p$, its dual or $S{L}_n^{\infty }$. We prove the following quantitative result: The identity operator on $W_n$ factors through any operator $T:W_N\to W_N$ which has large diagonal with respect to the Haar system, where $N$ depends \emph{linearly} on $n$.

12 pages

References in corpus (3)

• Factorization in mixed norm Hardy and BMO spaces
• Localization and projections on bi-parameter BMO
• Factorization in $S{L}^{\infty }$

Cited by in corpus (2)

• Continuous factorization of the identity matrix
• Orthogonal Factors of Operators on the Rosenthal $X_{p,w}$ spaces and the Bourgain-Rosenthal-Schechtman $R_{\omega }^p$ space