Journal of Convex Analysis 16 (2009), No. 2, 487--499
Copyright Heldermann Verlag 2009
Some Quantitative Interpolation Theorems under Lions-Peetre's Methods
Ming Fan
School of Industrial Technology and Management, Dalarna University, 781 88 Borlänge, Sweden
fmi@du.se
We formulate the quantitative version of interpolation theorems on compactness and weak compactness, the improved estimate for the k-uniform rotundity, and even the stability of the nearly uniform convexity under Lions-Peetre's interpolation methods of constants and means associated with quasi-power function parameters.
Keywords: Interpolation, k-uniform rotundity, Lions-Peetre's method, nearly uniform convexity, noncompactness, weak noncompactness.
MSC: 46B70, 46M35; 46B50, 47B07
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