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On a theorem of S. N. Bernstein and its application in modular function spaces. (English) Zbl 0693.46031

Function spaces, Proc. Int. Conf., Poznań/Poland 1986, Teubner-Texte Math. 103, 69-74 (1988).
[For the entire collection see Zbl 0673.00013.]
This note is connected with the well known Bernstein “lethargy” theorem. First, the author presents an interesting version of this theorem over a class of SF-spaces (Definition 2.1 and Theorem 2.4), and next considers its applications in the case of quasianalytic and quasientire functions in modular function spaces (Part 3).
Reviewer: A.Waszak

MSC:

46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Citations:

Zbl 0673.00013