Martingale transforms, the dyadic shift and the Hilbert transform: a sufficient condition for boundedness between matrix weighted spaces

2009/06/22 by Robert Kerr, Kerr, Robert
Mathematics · #42 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.0906.4028

openalex publication_date 2009/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show sufficient conditions on matrix weights U and V for the martingale transforms to be uniformly bounded from L²(V) to L²(U). We also show that these conditions imply the uniform boundedness of the dyadic shifts as well as the boundedness of the Hilbert transform between these spaces.

Citations

• Wavelets and the Angle between Past and Future

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