SOME EMBEDDING THEOREMS FOR GENERALIZED SOBOLEV SPACES,
Abstract:
The paper contains the detailed proofs of the collection of some embedding theorems for generalized Sobolev spaces as given in a paper by R. D. Meyer. Meyers paper resulted from a study of a partial differential operator which is elliptic on the interior of a closed bounded region Omega of the n-dimensional Euclidean space R sup n, and degenerates on the boundary of Omega. Thus one is led to study the functions in the spaces described in this paper. The first chapter of the paper presents the notation, the definitions of the various spaces and some elementary properties of generalized derivatives in the sense of Sobolev. Chapter II examines the embedding theorems of the spaces defined in Chapter I. Finally, Chapter III considers a result which is analogous to the Hahn-Banach theorem, that is, a norm bounding extension. Author