Analyticity and polynomial approximation in modular function spaces
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 \textit{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.
scientific article; zbMATH DE number 4132810
scientific article