The dyadic and the continuous Hilbert transforms with values in Banach spaces

2022/11/30 by Domelevo, Komla, Petermichl, Stefanie
#46B20 (Primary) 60G42 #60G44 #65C30 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · doi:10.48550/arxiv.2212.00090

Abstract

We show that if the Hilbert transform with values in a Banach space is L^p bounded, then so is the dyadic Hilbert transform, with a linear relation of the norms.

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