Spectral multipliers of self-adjoint operators on Besov and Triebel--Lizorkin spaces associated to operators

2018/11/15 by Bui, The Anh, Duong, Xuan Thinh · 2 citations
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1811.07712

Abstract

Let X be a space of homogeneous type and let L be a nonnegative self-adjoint operator on L²(X) which satisfies a Gaussian estimate on its heat kernel. In this paper we prove a Hömander type spectral multiplier theorem for L on the Besov and Triebel--Lizorkin spaces associated to L. Our work not only recovers the boundedness of the spectral multipliers on L^p spaces and Hardy spaces associated to L, but also is the first one which proves the boundedness of a general spectral theorem on Besov and Triebel--Lizorkin spaces.

Cited by

• On Hardy spaces associated with the twisted Laplacian and sharp estimates for the corresponding wave operator
• Fractional Heat Semigroup Characterization of Distances from Functions in Lipschitz Spaces to Their Subspaces

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