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Boundedness of Some Operators and Composition of Maximal Operators on Spaces of Homogeneous Type

Author: ZhangZuo
Tutor: HuGuoEn
School: PLA Information Engineering University
Course: Applied Mathematics
Keywords: Spaces of Homogeneous Type Singular integral Commutators Maximal Operators The Cotlar Type Inequality Weighted estimates Complex
CLC: O177
Type: Master's thesis
Year: 2009
Downloads: 6
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Abstract


Space of homogeneous type (X, d, μ) is defined on a set X endowed with a symmetric the proposed metric d and a non-negative regular Borel measure mu satisfy the double condition: there exists a constant C ≥ 1 such that for any x ∈ X and r GT; μ (B (x, 2r)) ≤ Cμ (B (x, r)) lt; ∞. wherein B (x, r) = {y ∈ X: d (x, y) lt; r} with x as the center, r is the radius of the ball. around the space of homogeneous type Calderón-Zygmund singular integrals with BMO functions commutators sector to commence the study. in standard nuclear conditions established Commutators of singular integrals Cotlar inequality in the weak nuclear conditions, with the Fefferman-Stein sharp maximal operator, weighted maximal singular integral commutators border proof of this paper has also established a very a singular integral operator Weighted Weak Endpoint Estimates for a conclusion of the Euclidean space associated with the Young function Maximal Operators extended to the space of homogeneous type on the second chapter of the work, when the singular integral operator of nuclear The function H (O | ¨) lder smooth conditions, the establishment of a singular integral commutators Cotlar type inequality as an application, using the inequality to prove the commutators weighted maximal singular integral bounded on two arguments meet. In addition, when the singular integral operators of nuclear function with respect to the first argument to satisfy the H (O | ¨) rmander smoothness conditions, the second change elements to meet the H (O | ¨) lder smooth conditions, with the help of Lorentz space, the establishment of maximal singular integral operator A weighted weak endpoint estimates. should be noted that the Cotlar type inequality established in this part, and the weak nuclear conditions Weighted Weak Endpoint Estimates, even in Euclidean space, but also new. main job is, when the singular integral operator kernel functions meet H (O | ¨) lder smoothness conditions on the first variable element, the second variant yuan to meet less smooth conditions, with the Fefferman-Stein sharp maximal operator M 0 # , s, prove the weighted maximal singular integral commutators bounded. the maximal abelian weighted estimated its nuclear function satisfy the weak nuclear conditions, even in Euclidean space, but also the new fourth chapter discusses the complex problem of the maximal operator associated with the Young function, Carrozza and Passarelli Di Napoli conclusions on the Euclidean space to promote attendance type space, improve and perfect the the Pérez and Wheeden a result. should be noted that, compared to with Pérez and Wheeden discussion, this paper proof is more concise.

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