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COMMUTATORS OF MULTIPLIER OPERATORS
作者姓名:Qian  Tao
作者单位:Department of
摘    要:Denote M~l={ω∈C~∞(R~K\{0}:|ω~((β))(ξ)|≤C_β|ξ|~(l-|β|)},l is an integer.R_((-α))~((m))is the n-foldcomposition of Taylor series remainder operator,m=(m_1,…,m_n)∈Z~n.Z is the set ofnon-negative integers,α∈(R~K)n.DenoteThe main results are as follows:(i) If γ_1,γ_2∈Z~K and l is an integer such that |γ_1|+|γ_2|+l=|m|=m_1+…+m_n,0≤|γ_1|≤{m_4},and ω∈M~l,then we havewhereis a conseant.(ii)In the same sense of notation as in (i),but now|m|=1,we havewhereThese results extend the corresponding ones given by coifman-Meyer in 4] andCohen,J.in 2],and,in a sense,extend those given by Calderón,A.P.in 1].

收稿时间:1983/8/10 0:00:00

Commutators of Multiplier Operators
Qian Tao.COMMUTATORS OF MULTIPLIER OPERATORS[J].Chinese Annals of Mathematics,Series B,1985,6(4):401-408.
Authors:Qian Tao
Institution:Department of Mathematics, Beijing University, Beijing, China.
Abstract:Denote M^l={w\in C^\infinity(R^K\{0}: |w^(\beta)(\xi)|\leq C_beta|xi|^l-|\beta|}, l is an integer.R^(m)_(\alpha) is the n-fold composition of Taylor series remainder operator, m = (m_1,\cdots, m_n)\in Z^n. Z is the set of non-negative integers, \alpha\in (R^K)^n.
Keywords:
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