Article
Keywords:
scales of Banach spaces; embedding theorems; predual to Campanato spaces; Sobolev-Campanato spaces
Summary:
We present definitions of Banach spaces predual to Campanato spaces and Sobolev-Campanato spaces, respectively, and we announce some results on embeddings and isomorphisms between these spaces. Detailed proofs will appear in our paper in Math. Nachr.
References:
                        
[1] S. Campanato: 
Proprietà di una famiglia di spazi funzionali. Ann. Scuola Norm. Sup. Pisa 18 (1964), 137–160. 
MR 0167862 | 
Zbl 0133.06801 
[2] J. A. Griepentrog: 
Zur Regularität linearer elliptischer und parabolischer Randwertprobleme mit nichtglatten Daten. Thesis, Humboldt-Universität zu Berlin, 2000. 
MR 1867697 | 
Zbl 0986.35030 
[3] K. Gröger, L. Recke: Preduals of Camapanato spaces and Sobolev-Campanato spaces: A general approach. Preprint 498 (1999), Weierstraß-Institut für Angewandte Analysis und Stochastik (to appear).
[4] O. A. Ladyshenskaya, N. N. Ural’tseva: Linear and Quasilinear Elliptic Equations. Nauka, Moskva, 1964, 1973. (Russian)
[6] J. M. Rakotoson: 
Equivalence between the growth of $\int _{B(x,r)}|\nabla u|^py$ and $T$ in the equation $P[u]=T$. J. Differ. Equations 86 (1990), 102–122. 
MR 1061892 | 
Zbl 0707.35033 
[9] G. Troianiello: 
Elliptic Differential Equations and Obstacle Problems. Plenum Press, New York, 1987. 
MR 1094820 | 
Zbl 0655.35002