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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Dimension dependence of factorization problems: Biparameter Hardy spaces
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by Richard Lechner PDF
Proc. Amer. Math. Soc. 147 (2019), 1639-1652 Request permission

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
  • 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
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 1639-1652
  • MSC (2010): Primary 46B07, 30H10, 46B25, 60G46
  • DOI: https://doi.org/10.1090/proc/14364
  • MathSciNet review: 3910428