Mixed martingale Hardy spaces

2019/11/13 by Szarvas, Kristóf, Weisz, Ferenc
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1911.05356

Abstract

In this paper we consider the martingale Hardy spaces defined with the help of the mixed L_\pv-norm. Five mixed martingale Hardy spaces will be investigated: H_\pv^s, H_\pv^S, H_\pv^M, \cP_\pv and \cQ_\pv. Several results are proved for these spaces, like atomic decompositions, Doob's inequality, boundedness, martingale inequalities and the generalization of the well-known Burkholder-Davis-Gundy inequality.

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