凸性模估计定理的推广

A Generalization for Estimation Theorem on Modulus of Convexity

本文证明了Ｌｐ（Ｘ）的凸性模δＬｐ（Ｘ）（ε）与Ｘ的凸性模δＸ（ε）之间有下列关系：ａδＸ（ｂεｐ／２）δＬｐ（Ｘ）（ε）δＸ（ε），（ｐ２）；ｃδＸ（ｄε）δＬｐ（Ｘ）（ε）δＸ（ε），（１＜ｐ２）．其中ａ，ｂ，ｃ，ｄ是正常数．

In this paper, we prove that the modulus of convexity for Banach spaces X and L p(X) satisfy the following inequalities: aδ X(bε p/2 )δ L p(X) (ε)δ X (ε), p2); cδ X(dε)δ L p(X) (ε)δ X (ε),(1<p2) . Where a,b,c and d are positive constants.