WIAS Preprint No. 498, (1999)

Preduals of Campanato spaces and Sobolev-Campanato spaces: A general construction


Authors

  • Gröger, Konrad
  • Recke, Lutz

2010 Mathematics Subject Classification

  • 46E35 46A13 46B10

Keywords

  • Projective and inductive systems of Banach spaces, imbedding theorems, equivalent norms

DOI

10.20347/WIAS.PREPRINT.498

Abstract

In this paper we describe two limiting processes for families of Banach spaces closely related to the standard definition of projective and inductive limits. These processes lead again to Banach spaces. Information about linear operators and duality between basic families of spaces is carried over to the corresponding limit spaces. The abstract results are shown to be applicable to Campanato spaces and Sobolev-Campanato spaces. In particular, we obtain the existence and a characterization of predual spaces. Some imbedding relations are investigated in more detail.

Appeared in

  • Math. Nachr., 230 (2001) pp. 45--72.

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