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Two Weights Weak Type for Fractional Integral Operators and Commutators

Author: ZhuHui
Tutor: ChenJianRen
School: Harbin Normal University
Course: Basic mathematics
Keywords: Fractional Integral Commutators Double weight weak type inequality Orlicz Function
CLC: O177.6
Type: Master's thesis
Year: 2010
Downloads: 16
Quote: 0
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Abstract


This paper studies the fractional integral operator and its high order commutators weight weak type inequality holds sufficient condition for the first chapter is an introduction section introduces the concept of fractional integral commutators , and existing the results of the simple conclusion second chapter gives a sufficient condition for fractional integral operator double weight weak ( p , q ) -type inequality holds Orlicz function Ap conditions set 0 lt ; alpha lt ; n , 1 lt ; p lt ; n / alpha / q = 1/p-α/n.Φ a Orlicz function and satisfy the △ 2 conditions , and its complementary function Ψ ∈ Bp (u, v ) is a pair of weight function if exist r GT ; 1 , for any cube Q satisfy the fractional integral operator Iα meet the dual weight weak ( p , q ) -type inequality is worth noting that Ap Bp conditions and △ meet any defined conditions Orlicz functions are established in Chapter Orlicz function for a given m ∈ N , given the high order commutators associated with the fractional integral operator Two-weight weak ( p , p ) -type inequality holds sufficient condition Let lt ; alpha lt ; n , 1 lt ; p <∞ , b ∈ BMO ( Rn ) , and ( u , v ) is a function of a pair of rights , and m ∈ N a r GT ; 1 and any cube Q, here is the fractional integral operator of higher order commutators Iαb m satisfy the dual weight weak ( p , p ) -type inequality .

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