Orlicz-Sobolev spaces and imbedding theorems. (English) Zbl 0216.15702


46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Full Text: DOI


[1] Clark, C. W., Introduction to Sobolev Spaces, (Seminar Notes (1968), University of British Columbia: University of British Columbia Vancouver) · Zbl 0337.92011
[2] Dankert, G., Sobolev Imbedding Theorems in Orlicz Spaces, (Thesis (1966), University of Cologne: University of Cologne Cologne) · Zbl 0191.41602
[3] Donaldson, T. K., Orlicz-Sobolev spaces and applications (1969), Department of Pure Mathematics, Australian National University: Department of Pure Mathematics, Australian National University Canberra · Zbl 0207.41501
[4] T. K. Donaldson; T. K. Donaldson · Zbl 0207.41501
[5] Dubinski, J. A., Some imbedding theorems in Orlicz spaces, Dokl. Akad. Nauk SSSR, 152, 529-532 (1963) · Zbl 0134.11303
[6] Krasnoselskii, M. A.; Rutickii, Y., Convex Functions and Orlicz Spaces (1961), Noordhoff: Noordhoff Groningen · Zbl 0095.09103
[7] Lions, J. L., Problèmes aux limites dans les équations aux derivées partielles (1966), University of Montreal Press · Zbl 0148.07801
[8] Meyers, N. G.; SerRin, J. B., \((H = W\), Proc. Nat. Acad. Sci. U.S.A., 51 (1964)), 1055-1056 · Zbl 0123.30501
[9] Morrey, C. B., Multiple Integral Problems in the Calculus of Variations (1966), Springer-Verlag: Springer-Verlag New York · Zbl 0108.10402
[10] Neças, J., Les méthodes directes en théorie des équations élliptiques (1967), Masson: Masson Paris · Zbl 1225.35003
[11] O’Neill, R., Fractional integration in Orlicz spaces, Trans. Amer. Math. Soc., 115, 300-328 (1965) · Zbl 0132.09201
[12] Serrin, J. B., Local behaviour of solutions of quasilinear equations, Acta Math., 113, 219-240 (1965) · Zbl 0173.39202
[13] Spanne, S., Some function spaces defined using the mean oscillation over cubes, Ann. Sc. Norm. Sup. Pisa, 19, 593-608 (1965) · Zbl 0199.44303
[14] Trudinger, N. S., On imbeddings into Orlicz spaces and applications, J. Math. Mech., 17, 473-484 (1967) · Zbl 0163.36402
[15] N. S. Trudinger; N. S. Trudinger · Zbl 0883.35035
[16] Zaanen, A. C., Linear Analysis (1953), Amsterdam-New York · Zbl 0053.25601
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.