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Bounded singular integral and fractional Commutators

Author: ZhouWeiJun
Tutor: MaBaiLin
School: Hunan University
Course: Basic mathematics
Keywords: Commutators Singular integral operator Fractional integral operator Hardy space Herz Space
CLC: O177
Type: Master's thesis
Year: 2003
Downloads: 105
Quote: 1
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Abstract


The article focuses on singular integral and fractional Multilinear Commutators bounded. The second chapter, the authors discuss the Multilinear Commutators on Hardy type spaces bounded. Set (?) = (B 1 b 2 ... the b m ), the b i ∈ BMO ( R n ), 1 ≤ i ≤ m, the multi linear commutators T the? Define for T ? (f) (x) = integral from R n (multiply from i = 1 to m ((b i (x)-b i (y)) K (x, y) f (y) dy)), where K (x, y) is Calderón-Zygmund nucleus. The chapter discusses operator T ? in the Hardy space H 1 / b, the weak Hardy space H ? ., 1, ∞ (R n < / sup>) and Herz type Hardy spaces HK q (?) 1 bounded. The third chapter, the author discusses the maximal multilinear commutators bounded. Chapter 1

E P (R n ) to L P F (R n ) bounded linear operators, E, F is a Banach space, b i ∈ BMO L (E, E) (R n ), i = 1,2, ..., m. And use it as a tool to prove the great multilinear commutators L P (R n ) bounded b i ∈ BMO (R n ), i = 1,2, ..., m. P = 1 case, we also got the great multi Commutators T ? * a weak type estimates. The fourth chapter, the author discusses Fractional Multilinear Commutators bounded. Set (?) = (B 1 , b to 2 , ... the b m ), the b i ∈ BMO (R n ), i = 1,2, ..., m. Standard fractional integral operator defined Multilinear Commutators This chapter first given acute the great count sub M # ([(?), The I a ) an estimate, which would prove the (?), the I a ] L p (R n ) to L q (R n ) of a bounded operator, where p, q satisfy 1

1) and Herz space, by means of the results, the authors proved a class of multi-linear commutators on Herz spaces bounded.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Functional Analysis
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