A maximal function characterisation of the Hardy space for the Gauss measure

2010/06/29 by Mauceri, G., Meda, S., Sjogren, P.
#42B25 #42B30 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1006.5551

Abstract

In dimension one we give a maximal function characterisation of the Hardy space H¹(g) for the Gauss measure g, introduced by G. Mauceri and S. Meda. In arbitrary dimension, we give a description of the nonnegative functions in H¹(g) and use it to prove that L^p(g) is a contained in H¹(g) for 1

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