Admissible decomposition for spectral multipliers on Gaussian L^p
arXiv:1608.03747 · doi:10.1007/s00209-017-1984-y
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.
11 pages