ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 46B70, 46M35 Ovchinnikov, Vladimir I., Voronezh State University, Russia Nonclassical Interpolation Theorems in Spaces of Smooth Functions The couple of spaces consisting of the space of bounded measurable functions and the space of functions with bounded generalized derivative on the real axis has not been studied extensively from the point of interpolation theory. The main results of the given work are interpolation theorems which extend the list of interpolation spaces for this couple. It turns out that the Triebel–Lizorkin spaces F_{∞,p}^{θ}(ℝ) for 0 < θ < 1 and 1 ≤ p ≤ ∞ are interpolation spaces for this couple, and they are obtained by methods different from the real or complex interpolation methods. These results come closer to answering the long standing problem of description of the complex method space between spaces of continuous and Lipschitz functions.