Dimensionless $L^p$ estimates for the Riesz vector on manifolds

Kamilia Dahmani; Komla Domelevo; Stefanie Petermichl

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arXiv · 1802.00366

Dimensionless $L^p$ estimates for the Riesz vector on manifolds

Kamilia Dahmani·Komla Domelevo·Stefanie Petermichl

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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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Kamilia Dahmani, Komla Domelevo, Stefanie Petermichl. 2018-02-01. Dimensionless $L^p$ estimates for the Riesz vector on manifolds. https://arxiv.org/abs/1802.00366

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