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arXiv · 1608.03747

Admissible decomposition for spectral multipliers on Gaussian L^p

Mikko Kemppainen
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Abstract

This paper concerns harmonic analysis of the Ornstein--Uhlenbeck operator L on the Euclidean space. We examine the method of decomposing a spectral multiplier ϕ(L) into three parts according to the notion of admissibility, which quantifies the doubling behaviour of the underlying Gaussian measure γ. We prove that the above-mentioned admissible decomposition is bounded in L^p(γ) for 1 < p \leq 2 in a certain sense involving the Gaussian conical square function. The proof relates admissibility with E. Nelson's hypercontractivity theorem in a novel way.

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Mikko Kemppainen. 2016-08-12. Admissible decomposition for spectral multipliers on Gaussian L^p. https://doi.org/10.1007/s00209-017-1984-y

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