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On the Sobolev spaces I. (English) Zbl 1052.46509
Summary: In this note, starting by Mikusinski’s definition of distributions (see J. Mikusinski and R. Sikorski [Théorie élémentaire des distributions. (Gauthier-Villars, Paris) (1964; Zbl 0155.10103)]), developed by the author [Bul. Inst. Politehn. Iaşi 17(21) no. 3-4, part I, 97-102 (1971; Zbl )], we present some characterizations of the Sobolev spaces by means of fundamental sequences and, finally, a direct proof of the Sobolev injection theorem.
MSC:
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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