Spectral Multipliers of Self-Adjoint Operators on Besov and Triebel–Lizorkin Spaces Associated to Operators
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Abstract Let $X$ be a space of homogeneous type and let $L$ be a nonnegative self-adjoint operator on $L^2(X)$ that satisfies a Gaussian estimate on its heat kernel. In this paper we prove a Hörmander-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 1st one that proves the boundedness of a general spectral multiplier theorem on Besov and Triebel–Lizorkin spaces.
2011 ◽
Vol 203
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pp. 109-122
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2014 ◽
Vol 91
(2)
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pp. 286-302
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2019 ◽
Vol 70
(2)
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pp. 197-246
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2011 ◽
Vol 63
(1)
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pp. 295-319
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2009 ◽
Vol 361
(12)
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pp. 6567-6582
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2021 ◽
Vol 13
(1)
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