Open AccessCommutators of BMO functions with spectral multiplier operators
Author(s) -
The Anh Bui
Publication year - 2012
Publication title -
journal of the mathematical society of japan
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.047
H-Index - 36
eISSN - 1881-1167
pISSN - 0025-5645
DOI - 10.2969/jmsj/06430885
Subject(s) - mathematics , multiplier (economics) , commutator , bounded function , semigroup , pure mathematics , homogeneous , operator (biology) , spectral theory , analytic semigroup , kernel (algebra) , mathematical analysis , discrete mathematics , hilbert space , algebra over a field , combinatorics , biochemistry , chemistry , lie conformal algebra , repressor , gene , transcription factor , economics , macroeconomics
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.18 page(s