Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Ming Fan

School of Industrial Technology and Management, Dalarna University, 781 88 Borlänge, Sweden

fmi@du.se

Keywords

  • Interpolation
  • k-uniform rotundity
  • Lions-Peetre's method
  • nearly uniform convexity
  • noncompactness
  • weak noncompactness

Mathematics Subject Classification

46B70, 46M35; 46B50, 47B07

Suggested citation

M. Fan. “Some Quantitative Interpolation Theorems under Lions-Peetre's Methods.” Journal of Convex Analysis 16 (2009), No. 2, 487–499.

Copyright Heldermann Verlag 2009