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ArticleOriginal scientific text

Title

Partial integral operators in Orlicz spaces with mixed norm

Authors 1, 2, 3

Affiliations

  1. Department of Mathematics, University of Würzburg, Am Hubland, D-97074 Würzburg, Germany
  2. Department of Mathematics, Pedagogical Institute of Lipetsk, ul. Lenina 42, R-398020 Lipetsk, Russian Federation
  3. Department of Mathematics, Belgosuniversity, Pr. Skoriny 4, BY-220050 Minsk, Belorussia

Keywords

ENG
Lebesgue space, ideal space, Orlicz space, partial integral operator, mixed norm

Bibliography

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  2. J. Bergh and J. Löfström , Interpolation Spaces-an Introduction, Springer, Berlin, 1976.
  3. G. Brack , Systems with substantially distributed parameters, in: Systems Analysis and Simulation I, Math. Res. 27, Akademie-Verlag, 1985, 421-424.
  4. A. B. Bukhvalov , Spaces of vector functions and tensor products, Sibirsk. Mat. Zh. 13 (1972), 1229-1238 (in Russian).
  5. A. B. Bukhvalov, On spaces with mixed norm, Vestnik Leningrad. Univ. 19 (1973), no. 4, 5-12 (in Russian).
  6. R. Bürger , On the maintenance of genetic variation: global analysis of Kimura's continuum-of-alleles model, J. Math. Biol. 24 (1986), 341-351.
  7. K. M. Case and P. F. Zweifel , Linear Transport Theory, Addison-Wesley, Reading, Mass., 1967.
  8. C. Cercignani , Mathematical Methods in Kinetic Theory, Macmillan, New York, 1969.
  9. A. S. Kalitvin , On some class of partial integral equations in aerodynamics, Sost. Persp. Razv. Nauchn.-Tekhn. Pot. Lipetsk. Obl. (Lipetsk) (1994), 210-212 (in Russian).
  10. A. S. Kalitvin and P. P. Zabreĭko , On the theory of partial integral operators, J. Integral Equations Appl. 3 (1991), 351-382.
  11. M. A. Krasnosel'skiĭ and Ya. B. Rutitskiĭ , Convex Functions and Orlicz Spaces, Fizmatgiz, Moscow, 1958 (in Russian); English transl.: Noordhoff, Groningen, 1961.
  12. M. A. Krasnosel'skiĭ, P. P. Zabreĭko, E. I. Pustyl'nik and P. E. Sobolevskiĭ, Integral Operators in Spaces of Summable Functions, Nauka, Moscow, 1966 (in Russian); English transl.: Noordhoff, Leyden, 1976.
  13. S. G. Kreĭn, Yu. I. Petunin and E. M. Semenov, Interpolation of Linear Operators, Nauka, Moscow, 1978 (in Russian); English transl.: Transl. Math. Monographs 54, Amer. Math. Soc., Providence, 1982.
  14. C. V. M. van der Mee , Transport theory in Lp spaces, Integral Equations Operator Theory 6 (1983), 405-443.
  15. I. N. Minin , Theory of Radiation Transfer in the Atmospheres of Planets, Nauka, Moscow, 1988 (in Russian).
  16. M. M. Rao and Z. D. Ren , Theory of Orlicz Spaces, Dekker, New York, 1991.
  17. Ya. B. Rutitskiĭ , New criteria for continuity and complete continuity of integral operators in Orlicz spaces, Izv. Vyssh. Uchebn. Zaved. Mat. 1962, no. 5 (30), 87-100.
  18. A. C. Zaanen , Linear Analysis, North-Holland, Amsterdam, 1953.
  19. P. P. Zabreĭko , Nonlinear integral operators, Voronezh. Gos. Univ. Trudy Sem. Funktsional. Anal. 1966, no. 8, 3-152 (in Russian).
  20. P. P. Zabreĭko, Ideal function spaces, Vestnik Yarosl. Univ. 8 (1974), 12-52 (in Russian).
Colloquium Mathematicum
1998/78/2
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Pages:
293-306
Main language of publication
English
Received
1997-10-02
Accepted
1997-10-02
Published
1998
Exact and natural sciences