Commutators of BMO functions with spectral multiplier operators
The Anh BUI
Source: J. Math. Soc. Japan Volume 64, Number 3
(2012), 885-902.
Abstract
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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Keywords: spectral multiplier theorems; non-negative self-adjoint operator; heat semigroup; space of homogeneous type
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Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1343133747
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Zentralblatt MATH identifier: 06090096
Mathematical Reviews number (MathSciNet): MR2965431
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