This paper contains threes chapters, the outline of the paper is arranged as follows:Chapter 1 presents the background and give out some necessary notations, definitions as well as some properties of operator.In chapter 2, introducing the result on Hardy-Littlewood maximal function of (?)-measurable operators and property of convexΦ-function, then we generalize the conclusions in [1] by replaced p-norm withΦ-norm. It contains two lemma and one theorem as bellow:(a) If (?), we have(b) If for t > 0, we have f*(|T|)(t) <∞. thenor(c) If T∈Lloc(Ðœ; (?)), then there is a constant C > 0, such thatIn these conclusions,Φis a moderate Young convex function, T is a measurable operator.Chapter 3 mainly generalize the conclusions in [2]: Let 1≤p <∞and let T be a sublinear operator acting on Lp(Ðœ;(?)) and L∞(Ðœ;(?)). letΦ-1(u) = u1/pÏ(u-1/p) for some concave functionÏ, we prove that noncommutative Orlicz spaces LΦ(Ðœ) is an interpolation sapce for sublinear operators T between Lp(Ðœ;(?)) and L∞(Ðœ;(?)), and...
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