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 MorreyHerz spaces BMO space Commutators 
CLC  O174 
Type  Master's thesis 
Year  2007 
Downloads  30 
Quotes  0 
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 (ω 1 ; ω 2 ) on nature , has been μΩ at K q α, p (ω 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 MorreyHerz 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 . }