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arXiv · 1811.07712

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

The Anh Bui·Xuan Thinh Duong
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Abstract

Let $X$ be a space of homogeneous type and let $L$ be a nonnegative self-adjoint operator on $L^2(X)$ which satisfies a Gaussian estimate on its heat kernel. In this paper we prove a H\"omander 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.

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The Anh Bui, Xuan Thinh Duong. 2018-11-15. Spectral multipliers of self-adjoint operators on Besov and Triebel--Lizorkin spaces associated to operators. https://arxiv.org/abs/1811.07712

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