## 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**
Ju A. Brudnyi and N. Ju Krugljak, - 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
M. Cwikel, M. Milman and J. Peetre, - 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**
J. Peetre, - 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**

*Real interpolation functors*, Soviet Math. Dokl.

**23**(1981), 5-8.

*Complex extrapolation*(in preparation).

*Banach couples*, Technical report, Lund, 1971. E. I. Pustylnik,

*On functions of a positive operator*, Math. USSR-Sb.

**47**(1984), 27-42.

## Additional Information

- © Copyright 1990 American Mathematical Society
- 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