The dyadic Riesz vector I

2023/09/06 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.2309.02802

Abstract

We derive a dyadic model operator for the Riesz vector. We show linear lower L^p bounds for 1 < p < ∞ between this model operator and the Riesz vector, when applied to functions with values in Banach spaces. By a lower bound we mean that the boundedness of the Riesz vector implies the boundedness of the dydic Riesz vector.

Related

• The dyadic Riesz vector II
• Dimensionless L^p estimates for the Riesz vector on manifolds
• Riesz transforms for Dirichlet spaces tamed by distributional curvature lower bounds
• On the sense of convergence in the dyadic representation theorem
• Local lower norm estimates for dyadic maximal operators and related Bellman functions