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Transactions of the American Mathematical Society

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The domain spaces of quasilogarithmic operators


Authors: M. Cwikel, B. Jawerth and M. Milman
Journal: Trans. Amer. Math. Soc. 317 (1990), 599-609
MSC: Primary 46M35
DOI: https://doi.org/10.1090/S0002-9947-1990-0974512-4
MathSciNet review: 974512
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Abstract: The construction of intermediate Banach spaces in interpolation theory and the study of commutator inequalities in this context are closely related to certain nonlinear operators $ \Omega $. Here an explicit characterization of the domain spaces of these operators $ \Omega $ is obtained, and the characterization is related to logarithmic Sobolev inequalities.


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  • [1] J. Bergh and J. Löfström, Interpolation spaces: An introduction, Springer-Verlag, Berlin, Heidelberg and New York, 1976. MR 0482275 (58:2349)
  • [2] Ju A. Brudnyi and N. Ju Krugljak, Real interpolation functors, Soviet Math. Dokl. 23 (1981), 5-8.
  • [3] C. P. Calderón and M. Milman, Interpolation of Sobolev spaces. The real method, Indiana Math. J. 32 (1983), 801-808. MR 721564 (85b:46039)
  • [4] M. Cwikel, $ K$-divisibility of the $ K$-functional and Calderón couples, Ark. Mat. 22 (1984), 39-62. MR 735877 (85m:46074)
  • [5] -, Monotonicity properties of interpolation spaces. II, Ark. Mat. 19 (1981), 123-136. MR 625541 (83a:46082)
  • [6] M. Cwikel, M. Milman and J. Peetre, Complex extrapolation (in preparation).
  • [7] L. Gross, Logarithmic Sobolev inequalities, Amer. J. Math. 97 (1975), 1061-1083. MR 0420249 (54:8263)
  • [8] J. Gustafsson, A function parameter in connection with interpolation of Banach spaces, Math. Scand. 42 (1978), 289-305. MR 512275 (80d:46124)
  • [9] S. Janson, Minimal and maximal methods of interpolation, J. Funct. Anal. 44 (1981), 50-73. MR 638294 (83j:46085)
  • [10] B. Jawerth, R. Rochberg and G. Weiss, Commutator and other second order estimates in real interpolation theory, Ark. Mat. 24 (1986), 191-219. MR 884187 (88i:46096)
  • [11] M. Milman, Complex interpolation and geometry of Banach spaces, Ann. Mat. Pura Appl. 86 (1984), 317-328. MR 765927 (86g:46024)
  • [12] V. I. Ovcinnikov, The method of orbits in interpolation theory, Math. Rep. 1 (1984), 349-516. MR 877877 (88d:46136)
  • [13] J. Peetre, Banach couples, Technical report, Lund, 1971.
  • [14] E. I. Pustylnik, On functions of a positive operator, Math. USSR-Sb. 47 (1984), 27-42.
  • [15] R. Rochberg and G. Weiss, Derivatives of analytic families of Banach spaces, Ann. of Math. 118 (1983), 315-347. MR 717826 (86a:46099)
  • [16] E. M. Stein and G. Weiss, Interpolation of operators with change of measures, Trans. Amer. Math. Soc. 87 (1958), 159-172. MR 0092943 (19:1184d)
  • [17] H. Triebel, Interpolation theory, function spaces, differential operators, North-Holland, Amsterdam, 1978. MR 503903 (80i:46032b)

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DOI: https://doi.org/10.1090/S0002-9947-1990-0974512-4
Article copyright: © Copyright 1990 American Mathematical Society

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