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


MSC:

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

References:

[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
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[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
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