Dimensionless L^p estimates for the Riesz vector on manifolds

2018/02/01 by Dahmani, Kamilia, Domelevo, Komla, Petermichl, Stefanie
#42B20 #60G44 #60G46 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1802.00366

Abstract

We present a new proof of the dimensionless L^p boundedness of the Riesz vector on manifolds with bounded geometry. Our proof has the significant advantage that it allows for a much stronger conclusion, namely that of a new dimensionless weighted L^p estimate with optimal exponent. Other than previous arguments, only a small part of our proof is based on special auxiliary functions, the core of the argument is a weak type estimate and a sparse decomposition of the stochastic process by X.D. Li, whose projection is the Riesz vector.

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