In this article,some necessary and sufficient conditions are shown in order that the inequality of the form Φ1(λ)Pu(f> λ) ≤ Ev(Φ2(C|f∞|)) holds with some constant C > 0 independent of martingale f =(fn)n≥...In this article,some necessary and sufficient conditions are shown in order that the inequality of the form Φ1(λ)Pu(f> λ) ≤ Ev(Φ2(C|f∞|)) holds with some constant C > 0 independent of martingale f =(fn)n≥0 and λ > 0,where Φ1 and Φ2 are a pair of Young functions,f = sup n≥0 |fn| and f∞ = lim n→∞ fn a.e.展开更多
In this article,we establish some atomic decomposition theorems for martingale Hardy-Lorentz spaces.As applications,with the help of weak atomic decompositions,some interpolation theorems for martingale Hardy-Lorentz ...In this article,we establish some atomic decomposition theorems for martingale Hardy-Lorentz spaces.As applications,with the help of weak atomic decompositions,some interpolation theorems for martingale Hardy-Lorentz spaces are proved.展开更多
In this article, some necessary and sufficient conditions are shown in order that weighted inequality of the form ■holds a.e. for uniformly integrable martingales f =(f_n)n≥0 with some constant C > 0,where Φ_1,...In this article, some necessary and sufficient conditions are shown in order that weighted inequality of the form ■holds a.e. for uniformly integrable martingales f =(f_n)n≥0 with some constant C > 0,where Φ_1,Φ_2 are Young functions, w_i(i = 1,2,3, 4) are weights, f~* =sup n≥0 |f_n| and f_∞=lim n→∞ f_n a.e. As an application, two-weight weak type maximal inequalities of martingales are considered, and particularly a new equivalence condition is presented.展开更多
文摘In this article,some necessary and sufficient conditions are shown in order that the inequality of the form Φ1(λ)Pu(f> λ) ≤ Ev(Φ2(C|f∞|)) holds with some constant C > 0 independent of martingale f =(fn)n≥0 and λ > 0,where Φ1 and Φ2 are a pair of Young functions,f = sup n≥0 |fn| and f∞ = lim n→∞ fn a.e.
基金supported by the National Natural Science Foundation of China(10871016)
文摘In this article,we establish some atomic decomposition theorems for martingale Hardy-Lorentz spaces.As applications,with the help of weak atomic decompositions,some interpolation theorems for martingale Hardy-Lorentz spaces are proved.
基金Supported by the National Natural Science Foundation of China(11871195)
文摘In this article, some necessary and sufficient conditions are shown in order that weighted inequality of the form ■holds a.e. for uniformly integrable martingales f =(f_n)n≥0 with some constant C > 0,where Φ_1,Φ_2 are Young functions, w_i(i = 1,2,3, 4) are weights, f~* =sup n≥0 |f_n| and f_∞=lim n→∞ f_n a.e. As an application, two-weight weak type maximal inequalities of martingales are considered, and particularly a new equivalence condition is presented.
