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July, 2012 Commutators of BMO functions with spectral multiplier operators
The Anh BUI
J. Math. Soc. Japan 64(3): 885-902 (July, 2012). DOI: 10.2969/jmsj/06430885


Let L be a non-negative self adjoint operator on L2(X) where X is a space of homogeneous type. Assume that L generates an analytic semigroup e-tL whose kernel satisfies the standard Gaussian upper bounds. By the spectral theory, we can define the spectral multiplier operator F(L). In this article, we show that the commutator of a BMO function with F(L) is bounded on Lp(X) for 1 < p < ∞ when F is a suitable function.


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The Anh BUI. "Commutators of BMO functions with spectral multiplier operators." J. Math. Soc. Japan 64 (3) 885 - 902, July, 2012.


Published: July, 2012
First available in Project Euclid: 24 July 2012

zbMATH: 1277.42014
MathSciNet: MR2965431
Digital Object Identifier: 10.2969/jmsj/06430885

Primary: 42B20
Secondary: 42B35 , 47B38

Keywords: heat semigroup , non-negative self-adjoint operator , space of homogeneous type , spectral multiplier theorems

Rights: Copyright © 2012 Mathematical Society of Japan


Vol.64 • No. 3 • July, 2012
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