Dissertation > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Theory of functions

The Properties of Marcinkiewicz Integral Operators and Commutators

Author XieRuLong
Tutor ShuLiSheng
School Anhui Normal University
Course Applied Mathematics
Keywords Marcinkiewicz integrals Weak Hardy Spaces Dini type condition Weighted Herz Spaces A1 right Morrey-Herz spaces BMO space Commutators
CLC O174
Type Master's thesis
Year 2007
Downloads 30
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This paper discusses the Marcinkiewicz integral operators and their commutators nature in the first chapter , we prove Marcinkiewicz integral operator μΩ is (H p, ∞ , L p, ∞ ) type of operator (0

n on the homogeneous function of zero second chapter we consider the Marcinkiewicz integral operator μΩ on Weighted Herz space K q α, p 1 ; ω 2 ) on nature , has been μΩ at K q α, p 1 ; ω 2 ) is bounded on , where ω 1 , ω 2 is a 1 weight function Let μ Ω, b m by Marcinkiewicz integral μΩ and BMO function b (x) to generate higher order commutators third chapter we study the Marcinkiewicz integral and its high order commutators on homogeneous Morrey-Herz spaces MK p , q α, λ on the continuity of the problem the last chapter of this paper we turn right parametric Marcinkiewicz integral μ Ω ρ the research proved that μ Ω ρ is (H p, ∞ , L p, ∞ ) ( 0

α conditions R n on the homogeneous function of zero for p = 1, weakened Ω conditions still obtain μ Ω ρ is (H 1, ∞ , L 1, ∞ ) type as a corollary of the above results were obtained μ Ω ρ is weak ( 1,1 ) -type operator .

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