【摘要】 本文证明了,在赋范线性空间(L_p(Ω),‖·‖L_p(Ω))中,用S_nf逼近f时,有如下结果: 或写成其中Ω_M=[0,M]×[0,M](M是任意大的正数),C_p为正的常数,ωA,p(f,t)是函数f∈L_p(Ω)的p范A光滑模,Ω=[0,∞)×[0,∞)更多还原

【Abstract】 In this paper the following result is proved as f is approximated by S_nf on the normed Linear Spaces(L_p（Ω）, ‖·‖_Lp（Ω）): ‖S_mf-f‖_Lp（ΩM）≤C_pω_A,p(f,1/(2^1/2)), or written to be ‖S_mf-f‖_Lp（Ωm）=O(ω_A,p(f,1/(n^1/2))where Ω_M=[0,M]×[0,M] （M is any positive number）, C_p is a positive constant, while ω_A,p（f,t） is the A-modulus of smoothness in thenorm of a function f ∈L_p（Ω）.更多还原