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Noncommutative weak Orlicz space T- measurable operators Hardy-Littlewood maximal function inequality

Author: YangJuan
Tutor: TuErDeBieKe
School: Xinjiang University
Course: Basic mathematics
Keywords: von Neumann algebra T- measurable operators Hardy-Littlewood maximal function Convex function Φ- norm Orlicz spaces Noncommutative Orlicz spaces
CLC: O178
Type: Master's thesis
Year: 2011
Downloads: 7
Quote: 0
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Abstract


This paper first gives noncommutative weak Orlicz space norm , then get the relevant non-commutative weak L P space inequality , finally got T- can be measured in the Hardy-Littlewood maximal function inequality and weak average weak Orlicz spaces non-commutative norm inequalities that the following three inequalities : (a) if 1 lt; P lt; ∞, yeah it has ‖ MT i α (T) ‖ L P ω ≦ A 0 ‖ T i α ‖ L P ω , for all T i α ∈ L P ω (M), (i = 0,1) (b) sup t gt; 0 Φ (t) λ t (MT ( | T |)) ≤ C Φsup t gt; 0 Φ (t) λ t (| T |), for all T ∈ L Φ ω (M). (c) Let Φ be a strictly convex function of limiting the growth of Young , take 1 lt; qΦ lt; pΦ lt; ∞, yeah Why there is a constant C Φ gt; 0, satisfy ‖ MT (| T |) ‖ L Φ ω ≤ C Φ < / sub> ‖ T ‖ L Φ ω , for all T ∈ L Φ ω (M).

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Inequality and other
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