Bulletin of the American Mathematical Society

MathSciNet review: 1567229
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Book Information:

Author: Hans Triebel
Title: Interpolation theory, function spaces, differential operators
Additional book information: North-Holland Publishing Company, Amsterdam, New York, Oxford, 1978, 528 pp., $66.75.

Colin Bennett, Banach function spaces and interpolation methods. II. Interpolation of weak-type operators, Linear operators and approximation, II (Proc. Conf., Math. Res. Inst., Oberwolfach, 1974) Internat. Ser. Numer. Math., Vol. 25, Birkhäuser, Basel, 1974, pp. 129–139. MR 0385535

Colin Bennett and Karl Rudnick, On Lorentz-Zygmund spaces, Dissertationes Math. (Rozprawy Mat.) 175 (1980), 67. MR 576995

Colin Bennett and Robert Sharpley, Weak-type inequalities for $H^{p}$ and BMO, Harmonic analysis in Euclidean spaces (Proc. Sympos. Pure Math., Williams Coll., Williamstown, Mass., 1978) Proc. Sympos. Pure Math., XXXV, Part, Amer. Math. Soc., Providence, R.I., 1979, pp. 201–229. MR 545259

A.-P. Calderón, Spaces between $L^{1}$ and $L^{\infty }$ and the theorem of Marcinkiewicz, Studia Math. 26 (1966), 273–299. MR 203444, DOI 10.4064/sm-26-3-301-304

R. Coifman, M. Cwikel, R. Rochberg, Y. Sagher, and G. Weiss, Complex interpolation for families of Banach spaces, Harmonic analysis in Euclidean spaces (Proc. Sympos. Pure Math., Williams Coll., Williamstown, Mass., 1978) Proc. Sympos. Pure Math., XXXV, Part, Amer. Math. Soc., Providence, R.I., 1979, pp. 269–282. MR 545314

Ronald A. DeVore, Sherman D. Riemenschneider, and Robert C. Sharpley, Weak interpolation in Banach spaces, J. Functional Analysis 33 (1979), no. 1, 58–94. MR 545385, DOI 10.1016/0022-1236(79)90018-1

R. DeVore and K. Scherer, Interpolation of linear operators on Sobolev spaces, Ann. of Math. (2) 109 (1979), no. 3, 583–599. MR 534764, DOI 10.2307/1971227

C. Fefferman, N. M. Rivière, and Y. Sagher, Interpolation between $H^{p}$ spaces: the real method, Trans. Amer. Math. Soc. 191 (1974), 75–81. MR 388072, DOI 10.1090/S0002-9947-1974-0388072-3

C. Fefferman and E. M. Stein, $H^{p}$ spaces of several variables, Acta Math. 129 (1972), no. 3-4, 137–193. MR 447953, DOI 10.1007/BF02392215

Tord Holmstedt, Interpolation of quasi-normed spaces, Math. Scand. 26 (1970), 177–199. MR 415352, DOI 10.7146/math.scand.a-10976

H. Johnen and K. Scherer, On the equivalence of the $K$-functional and moduli of continuity and some applications, Constructive theory of functions of several variables (Proc. Conf., Math. Res. Inst., Oberwolfach, 1976) Lecture Notes in Math., Vol. 571, Springer, Berlin, 1977, pp. 119–140. MR 0487423

Elias M. Stein, Interpolation of linear operators, Trans. Amer. Math. Soc. 83 (1956), 482–492. MR 82586, DOI 10.1090/S0002-9947-1956-0082586-0

E. M. Stein and Guido Weiss, An extension of a theorem of Marcinkiewicz and some of its applications, J. Math. Mech. 8 (1959), 263–284. MR 0107163, DOI 10.1512/iumj.1959.8.58019

1.

C. Bennett, Banach function spaces and interpolation methods II. Interpolation of weak type operators, Linear Operators and Approximation, Proceedings of the Oberwolfach Conference, 1974, Birkhäuser, Basel, pp. 129-140. MR 0385535

2.

C. Bennett and K. Rudnick, On Lorentz-Zygmund spaces, Dissertationes Math. (to appear). MR 576995

3.

C. Bennett and R. Sharpley, Weak-type inequalities for H, Proceedings of the Williamstown Conference on Harmonic Analysis, Proc. Sympos. Pure Math., vol. 35, Amer. Math. Soc., Providence, R. I., 1979, pp. 201-229. MR 545259

4.

A. P. Calderón, Spaces between L₁ and L_∞ and the theorem of Marcinkiewicz, Studia Math. 26 (1966), 273-299. MR 203444

5.

R. Coifman, M. Cwikel, R. Rochberg, Y. Sagher and G. Weiss, Complex interpolation for families of Banach spaces, Proceedings of the Williamstown Conference on Harmonic Analysis, Proc. Sympos. Pure Math., vol. 35, Amer. Math. Soc., Providence, R. I., 1979, pp. 269-282. MR 545314

6.

R. DeVore, S. Riemenschneider and R. Sharpley, Weak interpolation in Banach spaces, J. Functional Analysis (to appear). MR 545385

7.

R. DeVore and K. Scherer, Interpolation of linear operators on Sobolev spaces, Ann. of Math. (2) 109 (1979), 583-599. MR 534764

8.

C. Fefferman, N. Riviere and Y. Sagher, Interpolation between H: The real method, Trans. Amer. Math. Soc. 191 (1974), 75-81. MR 388072

9.

C. Fefferman and E. Stein, H, Acta Math. 129 (1972), 137-193. MR 447953

10.

T. Holmstedt, Interpolation of quasi-normed spaces, Math. Scand. 26 (1970), 177-199. MR 415352

11.

H. Johnen and K. Scherer, On the equivalence of the K-functional and moduli of continuity and some applications, Constructive Theory of Functions of Several Variables, Proceedings of the Oberwolfach Conference, 1976, Springer Lecture Notes no. 571, 119-140. MR 487423

12.

E. Stein, Interpolation of linear operators, Trans. Amer. Math. Soc. 83 (1956), 482-492. MR 82586

13.

E. Stein and G. Weiss, An extension of a theorem of Marcinkiewicz and some of its applications, J. Math. Mech. 8 (1959), 263-284. MR 107163