The domain spaces of quasilogarithmic operators

Cwikel, M.; Jawerth, B.; Milman, M.

doi:10.1090/S0002-9947-1990-0974512-4

The domain spaces of quasilogarithmic operators
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by M. Cwikel, B. Jawerth and M. Milman PDF

Trans. Amer. Math. Soc. 317 (1990), 599-609 Request permission

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.

References

Jöran Bergh and Jörgen Löfström, Interpolation spaces. An introduction, Grundlehren der Mathematischen Wissenschaften, No. 223, Springer-Verlag, Berlin-New York, 1976. MR 0482275

Real interpolation functors

23

Calixto P. Calderón and Mario Milman, Interpolation of Sobolev spaces. The real method, Indiana Univ. Math. J. 32 (1983), no. 6, 801–808. MR 721564, DOI 10.1512/iumj.1983.32.32054
Michael Cwikel, $K$-divisibility of the $K$-functional and Calderón couples, Ark. Mat. 22 (1984), no. 1, 39–62. MR 735877, DOI 10.1007/BF02384370
Michael Cwikel, Monotonicity properties of interpolation spaces. II, Ark. Mat. 19 (1981), no. 1, 123–136. MR 625541, DOI 10.1007/BF02384473

Complex extrapolation

Leonard Gross, Logarithmic Sobolev inequalities, Amer. J. Math. 97 (1975), no. 4, 1061–1083. MR 420249, DOI 10.2307/2373688
Jan Gustavsson, A function parameter in connection with interpolation of Banach spaces, Math. Scand. 42 (1978), no. 2, 289–305. MR 512275, DOI 10.7146/math.scand.a-11754
Svante Janson, Minimal and maximal methods of interpolation, J. Functional Analysis 44 (1981), no. 1, 50–73. MR 638294, DOI 10.1016/0022-1236(81)90004-5
Björn Jawerth, Richard Rochberg, and Guido Weiss, Commutator and other second order estimates in real interpolation theory, Ark. Mat. 24 (1986), no. 2, 191–219. MR 884187, DOI 10.1007/BF02384398
Mario Milman, Complex interpolation and geometry of Banach spaces, Ann. Mat. Pura Appl. (4) 136 (1984), 317–328. MR 765927, DOI 10.1007/BF01773388
V. I. Ovchinnikov, The method of orbits in interpolation theory, Math. Rep. 1 (1984), no. 2, i–x and 349–515. MR 877877

Banach couples

On functions of a positive operator

47

Richard Rochberg and Guido Weiss, Derivatives of analytic families of Banach spaces, Ann. of Math. (2) 118 (1983), no. 2, 315–347. MR 717826, DOI 10.2307/2007031
E. M. Stein and G. Weiss, Interpolation of operators with change of measures, Trans. Amer. Math. Soc. 87 (1958), 159–172. MR 92943, DOI 10.1090/S0002-9947-1958-0092943-6
H. Triebel, Interpolation theory, function spaces, differential operators, VEB Deutscher Verlag der Wissenschaften, Berlin, 1978. MR 500580