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Endpoint Estimates for Commutators of Singular Integral Operators

Author: QiaoDan
Tutor: ChenJianRen
School: Harbin Normal University
Course: Basic mathematics
Keywords: Singular integral operator Commutators Dramatically higher order commutators Double Young function Sharp maximal function
CLC: O177.6
Type: Master's thesis
Year: 2011
Downloads: 10
Quote: 0
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Abstract


In this thesis, the different types of nuclear singular integral operator commutators on Lp (Rn) space and Hardy space bounded text is divided into three chapters . The first chapter is the introduction , the singular integral operator commutators and some the derived basic concepts , and the existing conclusions were simple summary . chapter greatly by the Calderon-Zygmund singular integral operators with BMO functions generated higher order commutators Tb , m *. Through its Sharp maximal function estimates , pointing out that they only satisfy the inequality L (log L) m and Lp (Rn ) ( lt ; p lt; ∞ ) bounded by conditions in Chapter the ∫ 01ωq ( δ) / δdδ lt ; ∞ replaced by a stronger Dini conditions : the ∫ 01ωq ( δ ) / δlog1/δdδ lt ; ∞ Lq-Dini -type nuclear ( lt ; q lt ; ∞ ) singular integral operator exchange sub [ b , T ] satisfy L (logL) type inequality given estimates on Hardy spaces , and these results to the case of the higher order commutators .

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