Dissertation
Dissertation > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Functional Analysis > Integral transforms and operational calculus

Meet a Class H (?) Rmander type condition singular integral operator and its boundedness of commutators

Author ZhangDaiQing
Tutor ZhangZuo
School Heilongjiang University
Course Basic mathematics
Keywords singular integral operator multilinear commutator variant H(o ¨)rmander condition Lipschitz function Hardy type space BMO space A_p weight
CLC O177.6
Type Master's thesis
Year 2011
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This thesis contains four chapters, we mainly discuss the weighted bounded-ness of singular integral operator satisfying a variant Hormander’s condition, and the boundednesses of its commutators generated by the Lipschitz function and mul-tilinear commutator generated by the BMO function.In Chapter 1, we introduce the definition, notation and development of the sin-gular integral operator satisfying a variant Hormander’s condition, and put forward the questions to be studied. In Chapter 2, we prove the boundedness for commuta-tor generated by the Lipschitz function with the singular integral operator satisfying a variant Hormander’s condition on Lebesgue spaces and Hardy type spaces. In Chapter 3, we study the weighted weak type estimates for the multilinear commu-tator generated by the singular integral operator satisfying a variant Hormander’s condition with the BMO function. In Chapter 4, We discuss the weighted (p,p) boundedness and the weighted weak (1,1) boundedness for the singular integral operator satisfying a variant LT-Hormander’s condition.

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