Analyticity and polynomial approximation in modular function spaces. (English) Zbl 0692.41010

Let E be a compact subset of \(C^ n\) and let \(L_ p\) be a modular functions space. The authors study the problem of analytic extension of \(f\in L_ p\) to a holomorphic function by means of polynomial approximations. The class of modular functions studied here is a large one that contains Orlicz spaces. The results proved generalize some of the results of W. Plesniak [Proc. Int. Conf., Gdansk 1979, 558-571 (1981; Zbl 0487.41045)] for Orlicz spaces and some other earlier results of the authors [‘Function spaces’, Proc. Int. Conf. Poznań/Poland 1986, Teubner-Texte Math. 103, 63-68 (1988)] for s-convex function modulars.
Reviewer: G.D.Dikshit


41A10 Approximation by polynomials
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)


Zbl 0487.41045
Full Text: DOI


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