In this paper we proved the A_(p)-weighted inequalities for martingale transforms and differential subordinations of Banach-space-valued regular maringales.We discussed the relations between the weighted inequalities,...In this paper we proved the A_(p)-weighted inequalities for martingale transforms and differential subordinations of Banach-space-valued regular maringales.We discussed the relations between the weighted inequalities,A_(p)-weight functions and the Banach spaces which has the UMD property or are isomorphic to Hilbert space.展开更多
In this paper we define some weak martingale Hardy spaces and three kinds of weak atoms.They are the counterparts of martingale Hardy spaces and atoms in the classical martingale Hp-theory.And then three atomic decomp...In this paper we define some weak martingale Hardy spaces and three kinds of weak atoms.They are the counterparts of martingale Hardy spaces and atoms in the classical martingale Hp-theory.And then three atomic decomposition theorems for martingales in weak martingale Hardy spaces are proved.With the help of the weak atomic decompositions of martingale,a sufficient condition for a sublinear operator defined on the weak martingale Hardy spaces to be bounded is given.Using the sufficient condition,we obtain a series of martingale inequalities with respect to the weak L_(p)-norm,the inequalities of weak(p,p)-type and some continuous imbedding relationships between various weak martingale Hardy spaces.These inequalities are the weak versions of the basic inequalities in the classical martingale H_(p)-theory.展开更多
Abstract Let x = （xn）n≥1 be a martingale on a noncommutative probability space （М,τ） and （Wn）n≥1 a sequence of positive numbers such that Wn =∑^n_k=1 wk→∞ as n→∞. We prove that x = （Xn）n≥1 converges...Abstract Let x = （xn）n≥1 be a martingale on a noncommutative probability space （М,τ） and （Wn）n≥1 a sequence of positive numbers such that Wn =∑^n_k=1 wk→∞ as n→∞. We prove that x = （Xn）n≥1 converges bilaterally almost uniformly （b.a.u.） if and only if the weighted average （σan（x））n≥1 of x converges b.a.u, to the same limit under some condition, where σn（x） is given by σn（x）=1/Wn ^n∑_k=1 wkxk,n=1,2,… Furthermore, we prove that x = （xn）n≥1 converges in Lp（М） if and only if （σ＇n（x））n≥1 converges in Lp（М）, where 1 ≤p 〈 ∞ .We also get a criterion of uniform integrability for a family in L1（М）.展开更多
In this paper,the weak Orlicz space wLΦis introduced and its applications to the martingale theory are discussed.In particular,a series of martingale inequalities including the maximal function inequality in weak Orl...In this paper,the weak Orlicz space wLΦis introduced and its applications to the martingale theory are discussed.In particular,a series of martingale inequalities including the maximal function inequality in weak Orlicz spaces are established;the relationships between these spaces are investigated.Moreover,the boundedness of several sublinear operators from one weak Orlicz space to another is proved;their vector-valued analogues are also considered.展开更多
文摘In this paper we proved the A_(p)-weighted inequalities for martingale transforms and differential subordinations of Banach-space-valued regular maringales.We discussed the relations between the weighted inequalities,A_(p)-weight functions and the Banach spaces which has the UMD property or are isomorphic to Hilbert space.
基金supported by National Natural Science Foundation of China(Grant No.10371093).
文摘In this paper we define some weak martingale Hardy spaces and three kinds of weak atoms.They are the counterparts of martingale Hardy spaces and atoms in the classical martingale Hp-theory.And then three atomic decomposition theorems for martingales in weak martingale Hardy spaces are proved.With the help of the weak atomic decompositions of martingale,a sufficient condition for a sublinear operator defined on the weak martingale Hardy spaces to be bounded is given.Using the sufficient condition,we obtain a series of martingale inequalities with respect to the weak L_(p)-norm,the inequalities of weak(p,p)-type and some continuous imbedding relationships between various weak martingale Hardy spaces.These inequalities are the weak versions of the basic inequalities in the classical martingale H_(p)-theory.
基金supported by National Natural Science Foundation of China (Grant No.11071190)
文摘Abstract Let x = （xn）n≥1 be a martingale on a noncommutative probability space （М,τ） and （Wn）n≥1 a sequence of positive numbers such that Wn =∑^n_k=1 wk→∞ as n→∞. We prove that x = （Xn）n≥1 converges bilaterally almost uniformly （b.a.u.） if and only if the weighted average （σan（x））n≥1 of x converges b.a.u, to the same limit under some condition, where σn（x） is given by σn（x）=1/Wn ^n∑_k=1 wkxk,n=1,2,… Furthermore, we prove that x = （xn）n≥1 converges in Lp（М） if and only if （σ＇n（x））n≥1 converges in Lp（М）, where 1 ≤p 〈 ∞ .We also get a criterion of uniform integrability for a family in L1（М）.
基金supported by National Natural Science Foundation of China(Grant No.10671147)
文摘In this paper,the weak Orlicz space wLΦis introduced and its applications to the martingale theory are discussed.In particular,a series of martingale inequalities including the maximal function inequality in weak Orlicz spaces are established;the relationships between these spaces are investigated.Moreover,the boundedness of several sublinear operators from one weak Orlicz space to another is proved;their vector-valued analogues are also considered.
