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arXiv · 1802.02857

Dimension dependence of factorization problems: Hardy spaces and $SL_n^\infty$

Richard Lechner
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Abstract

Given $1 \leq p < \infty$, let $W_n$ denote the finite-dimensional dyadic Hardy space $H_n^p$, its dual or $SL_n^\infty$. 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 $n$.

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Richard Lechner. 2018-02-08. Dimension dependence of factorization problems: Hardy spaces and $SL_n^\infty$. https://doi.org/10.1007/s11856-019-1883-5

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