Criteria for extreme points and strongly extreme points in Musielak-Orliczsequence spaces, equipped with both the Luxemburg norm and the Orlicz norm, are given.
Let （Ω,μ） be a a-finite measure space and Φ ： Ω × [0,∞） → [0, ∞] be a Musielak-Orlicz function. Denote by L^Φ（Ω） the Musielak-Orlicz space generated by Φ. We prove that the Amemiya norm equals the...Let （Ω,μ） be a a-finite measure space and Φ ： Ω × [0,∞） → [0, ∞] be a Musielak-Orlicz function. Denote by L^Φ（Ω） the Musielak-Orlicz space generated by Φ. We prove that the Amemiya norm equals the Orlicz norm in L^Φ（Ω）.展开更多
The aim of this paper is to establish several necessary and sufficient conditions in order that the weighted inequality ρ（M f 〉 λ）Φ（λ） ≤ C ∫_Ω~Ψ （C｜f｜）σdμ,λ 〉 0 or ρ（Mf〉λ） ≤ C∫-Ω~Φ（Cλ^...The aim of this paper is to establish several necessary and sufficient conditions in order that the weighted inequality ρ（M f 〉 λ）Φ（λ） ≤ C ∫_Ω~Ψ （C｜f｜）σdμ,λ 〉 0 or ρ（Mf〉λ） ≤ C∫-Ω~Φ（Cλ^-1 ｜f｜）σdμ,λ 〉0 holds for every uniformly integral martingale f=（f_n）, where M is the Doob＇s maximal operator, Φ, Ψ are both Φ-functions, and e, σ are weights.展开更多
In Orlicz-Lorentz sequence space Aψ,w with the Orlicz norm, uniform monotonic- ity, points of upper local uniform monotonicity and lower local uniform monotonicity are characterized. Moreover, the monotonicity coeffi...In Orlicz-Lorentz sequence space Aψ,w with the Orlicz norm, uniform monotonic- ity, points of upper local uniform monotonicity and lower local uniform monotonicity are characterized. Moreover, the monotonicity coefficient in Aψ,w are discussed.展开更多
众所周知,Orlicz范数与Luxemburg范数是等价的。2011年,BANG H H,HOANG N V,HUY V N,研究了由N函数生成的Orlicz空间中Orlicz范数与Luxemburg范数等价的最佳常数,本文将他们的结果推广到由一般Orlicz函数中Orlicz范数与Luxemburg范数等...众所周知,Orlicz范数与Luxemburg范数是等价的。2011年,BANG H H,HOANG N V,HUY V N,研究了由N函数生成的Orlicz空间中Orlicz范数与Luxemburg范数等价的最佳常数,本文将他们的结果推广到由一般Orlicz函数中Orlicz范数与Luxemburg范数等价的最佳常数。与此同时得到了1<inf k>0∶1 k(1+IΦ(kx))=1及sup k>0∶1 k(1+IΦ(kx))=1<∞的等价条件。展开更多
基金This research is supported by the National Natural Science Foundation of China(No.10001010)the Youth Foundation of Education Department of Heilongjiang(No.10541099)
文摘Criteria for extreme points and strongly extreme points in Musielak-Orliczsequence spaces, equipped with both the Luxemburg norm and the Orlicz norm, are given.
基金Project supported by National Natural Science Foundation of China(10371052,10671084)
文摘Let （Ω,μ） be a a-finite measure space and Φ ： Ω × [0,∞） → [0, ∞] be a Musielak-Orlicz function. Denote by L^Φ（Ω） the Musielak-Orlicz space generated by Φ. We prove that the Amemiya norm equals the Orlicz norm in L^Φ（Ω）.
基金Supported by the National Natural Science Foundation of China (1067114711071190)
文摘The aim of this paper is to establish several necessary and sufficient conditions in order that the weighted inequality ρ（M f 〉 λ）Φ（λ） ≤ C ∫_Ω~Ψ （C｜f｜）σdμ,λ 〉 0 or ρ（Mf〉λ） ≤ C∫-Ω~Φ（Cλ^-1 ｜f｜）σdμ,λ 〉0 holds for every uniformly integral martingale f=（f_n）, where M is the Doob＇s maximal operator, Φ, Ψ are both Φ-functions, and e, σ are weights.
基金supported by the National Science Foundation of China(11271248 and 11302002)the National Science Research Project of Anhui Educational Department(KJ2012Z127)the PhD research startup foundation of Anhui Normal University
文摘In Orlicz-Lorentz sequence space Aψ,w with the Orlicz norm, uniform monotonic- ity, points of upper local uniform monotonicity and lower local uniform monotonicity are characterized. Moreover, the monotonicity coefficient in Aψ,w are discussed.
文摘众所周知,Orlicz范数与Luxemburg范数是等价的。2011年,BANG H H,HOANG N V,HUY V N,研究了由N函数生成的Orlicz空间中Orlicz范数与Luxemburg范数等价的最佳常数,本文将他们的结果推广到由一般Orlicz函数中Orlicz范数与Luxemburg范数等价的最佳常数。与此同时得到了1<inf k>0∶1 k(1+IΦ(kx))=1及sup k>0∶1 k(1+IΦ(kx))=1<∞的等价条件。
