Independent sums of H¹_n(\mathbbT) and H¹_n(δ)

2015/05/13 by Maciej Rzeszut, Rzeszut, Maciej, Michał Wojciechowski +1
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1505.06511

openalex publication_date 2015/05/13 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We construct a new idempotent Fourier multiplier on the Hardy space on the bidisc, which could not be obtained by applying known one dimentional results. The main tool is a new L¹ equivalent of the Stein martingale inequality which holds for a special filtration of periodic subsets of \mathbbT with some restrictions on the functions involved. We also identify the isomorphic type of the range of the associated operator as the independent sum of dyadic H¹_n, which is known to be a complemented and invariant subspace of dyadic H¹.

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