The theme in this article is the inequalities of B_valued martingales and the properties of Banach spaces. In utilising the techniques of rearranged functions, we proved that for a martingale f we have ‖M αf‖ Φ...The theme in this article is the inequalities of B_valued martingales and the properties of Banach spaces. In utilising the techniques of rearranged functions, we proved that for a martingale f we have ‖M αf‖ Φ≤C pΦ ‖f # α‖ Φ and the same result for (Mf,S (p) (f)+D ∞), (Mf∧Sf,Mf∧Sf+D ∞). This contains the results in R.L.Long[1], furthermore, some of the inequalities can be used to describe the properties of Banach spaces.展开更多
Let φ be an Orlicz function that has a complementary function φ＊ and let lφ be an Orlicz sequence space. We prove a similar version of Rearrangement Inequality and Chebyshev＇s Sum Inequality in lφ FX, the Freml...Let φ be an Orlicz function that has a complementary function φ＊ and let lφ be an Orlicz sequence space. We prove a similar version of Rearrangement Inequality and Chebyshev＇s Sum Inequality in lφ FX, the Fremlin projective tensor product of lφ with a Banach lattice X, and in lφ iX, the Wittstock injective tensor product of lφ with a Banach lattice X.展开更多
In this paper the operator-valued martingale transform inequalities in rearrangement invariant function spaces are proved.Some well-known results are generalized and unified.Applications are given to classical operato...In this paper the operator-valued martingale transform inequalities in rearrangement invariant function spaces are proved.Some well-known results are generalized and unified.Applications are given to classical operators such as the maximal operator and the p-variation operator of vector-valued martingales,then we can very easily obtain some new vector-valued martingale inequalities in rearrangement invariant function spaces.These inequalities are closely related to both the geometrical properties of the underlying Banach spaces and the Boyd indices of the rearrangement invariant function spaces.Finally we give an equivalent characterization of UMD Banach lattices,and also prove the Fefferman-Stein theorem in the rearrangement invariant function spaces setting.展开更多
文摘The theme in this article is the inequalities of B_valued martingales and the properties of Banach spaces. In utilising the techniques of rearranged functions, we proved that for a martingale f we have ‖M αf‖ Φ≤C pΦ ‖f # α‖ Φ and the same result for (Mf,S (p) (f)+D ∞), (Mf∧Sf,Mf∧Sf+D ∞). This contains the results in R.L.Long[1], furthermore, some of the inequalities can be used to describe the properties of Banach spaces.
文摘Let φ be an Orlicz function that has a complementary function φ＊ and let lφ be an Orlicz sequence space. We prove a similar version of Rearrangement Inequality and Chebyshev＇s Sum Inequality in lφ FX, the Fremlin projective tensor product of lφ with a Banach lattice X, and in lφ iX, the Wittstock injective tensor product of lφ with a Banach lattice X.
基金supported by National Natural Science Foundation of China (GrantNo. 11001273)Research Fund for International Young Scientists (Grant No. 11150110456)+1 种基金Research Fundfor the Doctoral Program of Higher Education of China (Grant No. 20100162120035)Postdoctoral Science Foundation of China and Central South University
文摘In this paper the operator-valued martingale transform inequalities in rearrangement invariant function spaces are proved.Some well-known results are generalized and unified.Applications are given to classical operators such as the maximal operator and the p-variation operator of vector-valued martingales,then we can very easily obtain some new vector-valued martingale inequalities in rearrangement invariant function spaces.These inequalities are closely related to both the geometrical properties of the underlying Banach spaces and the Boyd indices of the rearrangement invariant function spaces.Finally we give an equivalent characterization of UMD Banach lattices,and also prove the Fefferman-Stein theorem in the rearrangement invariant function spaces setting.
