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Dimension dependence of factorization problems: Biparameter Hardy spaces


Author: Richard Lechner
Journal: Proc. Amer. Math. Soc. 147 (2019), 1639-1652
MSC (2010): Primary 46B07, 30H10, 46B25, 60G46
DOI: https://doi.org/10.1090/proc/14364
Published electronically: January 8, 2019
MathSciNet review: 3910428
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Abstract: Given $1 \leq p,q < \infty$, and $n\in \mathbb {N}_0$, let $H_n^p(H_n^q)$ denote the finite-dimensional building blocks of the biparameter dyadic Hardy space $H^p(H^q)$. Let $(V_n : n\in \mathbb {N}_0)$ denote either $\bigl (H_n^p(H_n^q) : n\in \mathbb {N}_0\bigr )$ or $\bigl ( (H_n^p(H_n^q))^* : n\in \mathbb {N}_0\bigr )$. We show that the identity operator on $V_n$ factors through any operator $T : V_N\to V_N$ which has a large diagonal with respect to the Haar system, where $N$ depends linearly on $n$.


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Additional Information

Richard Lechner
Affiliation: Institute of Analysis, Johannes Kepler University Linz, Altenberger Strasse 69, A-4040 Linz, Austria
MR Author ID: 1058338
Email: richard.lechner@jku.at

Keywords: Factorization, local theory, almost-diagonalization, classical Banach spaces, Hardy spaces, BMO
Received by editor(s): February 20, 2018
Received by editor(s) in revised form: August 14, 2018
Published electronically: January 8, 2019
Additional Notes: This work was supported by the Austrian Science Foundation (FWF) Pr.Nr. P28352.
Communicated by: Stephen Dilworth
Article copyright: © Copyright 2019 American Mathematical Society