大学数学
大學數學
대학수학
COLLEGE MATHEMATICS
2008年
2期
37-43
,共7页
参数型Marcinkiewicz积分%弱Hardy空间%Lipα条件%Dini型条件
參數型Marcinkiewicz積分%弱Hardy空間%Lipα條件%Dini型條件
삼수형Marcinkiewicz적분%약Hardy공간%Lipα조건%Dini형조건
parametric Marcinkiewicz integral%weak Hardy space%Lipα condition%Dini-type condition
证明了参数型Marcinkiewicz积分μΝΩ是(Hp,∞,Lp,∞)(0＜p≤1)型的算子,这里Ω是满足Lipα条件的Rn上的零次齐次函数.对于p=1,减弱了Ω的条件仍得到μpΩ是(H1,∞,L1,∞)型的.作为上述结果的推论,得到了μρΩ是弱(1,1)型的算子.
證明瞭參數型Marcinkiewicz積分μΝΩ是(Hp,∞,Lp,∞)(0＜p≤1)型的算子,這裏Ω是滿足Lipα條件的Rn上的零次齊次函數.對于p=1,減弱瞭Ω的條件仍得到μpΩ是(H1,∞,L1,∞)型的.作為上述結果的推論,得到瞭μρΩ是弱(1,1)型的算子.
증명료삼수형Marcinkiewicz적분μΝΩ시(Hp,∞,Lp,∞)(0＜p≤1)형적산자,저리Ω시만족Lipα조건적Rn상적령차제차함수.대우p=1,감약료Ω적조건잉득도μpΩ시(H1,∞,L1,∞)형적.작위상술결과적추론,득도료μρΩ시약(1,1)형적산자.
we prove that the parametric Marcinkiewicz integralμρΩis an operator of type (Hp,∞,Lp,∞)(0＜p≤1),if Ω∈Lipα is a homogeneous function of degree zero.For p=1,we weaken the smoothness condition assumed on Ω and again obtain μρΩ is of type (H1,∞,L1,∞).As a corollary of the results above,we give the weak type(1,1) boundedness of μpΝΩ.
