Banach April 2018

banach@mathdept.okstate.edu

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Abstract of a paper by Richard Lechner
by Bentuo Zheng (bzheng) 01 Apr '18

01 Apr '18

This is an announcement for the paper “Factorization in mixed norm Hardy and BMO spaces” by Richard Lechner<https://arxiv.org/find/math/1/au:+Lechner_R/0/1/0/all/0/1>. Abstract: Let $1\leq p, q<\infty$ and $1\leq r\leq\infty$. We show that the direct sum of mixed norm Hardy spaces $(\sum_n H_n^p(H_n^q))_r$ and the sum of their dual spaces $(\sum_n H_n^p(H_n^q)^*)_r$ are both primary. We do so by using Bourgain's localization method and solving the finite dimensional factorization problem. In particular, we obtain that the spaces $(\sum_n H_n^1(H_n^s))_r, (\sum_n H_n^1(H_n^s))_r)$, as well as $(\sum_n BMO_n(H_n^s))_r$ and $(\sum_n H_n^s(BMO_n))_r$, $1<s<\infty, 1\leq r\leq\infty$ are all primary.. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1610.01506

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Abstract of a paper by Richard Lechner
by Bentuo Zheng (bzheng) 01 Apr '18

01 Apr '18

This is an announcement for the paper “Dimension dependence of factorization problems: Hardy spaces and $SL_n^{\infty}$” by Richard Lechner<https://arxiv.org/find/math/1/au:+Lechner_R/0/1/0/all/0/1>. 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 $T: W_N\rightarrow W_N$ which has large diagonal with respect to the Haar system, where $N$ depends \emph{linearly} on $n$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1802.02857

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Banach April 2018