Book Review
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MathSciNet review:
1568114
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Book Information:
Author:
Hans Triebel
Title:
Theory of function spaces II
Additional book information:
Birkh\"auser Verlag, Basel, 1992, viii+370 pp., US$117{.}00. ISBN 3-7643-2639-5.
D. L. Burkholder, R. F. Gundy, and M. L. Silverstein, A maximal function characterization of the class $H^{p}$, Trans. Amer. Math. Soc. 157 (1971), 137–153. MR 274767, DOI 10.1090/S0002-9947-1971-0274767-6
A. Baernstein II and E. T. Sawyer, Embedding and multiplier theorems for $H^P(\textbf {R}^n)$, Mem. Amer. Math. Soc. 53 (1985), no. 318, iv+82. MR 776176, DOI 10.1090/memo/0318
A.-P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113–190. MR 167830, DOI 10.4064/sm-24-2-113-190
R. R. Coifman, Y. Meyer, and E. M. Stein, Some new function spaces and their applications to harmonic analysis, J. Funct. Anal. 62 (1985), no. 2, 304–335. MR 791851, DOI 10.1016/0022-1236(85)90007-2
F. M. Christ and M. I. Weinstein, Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation, J. Funct. Anal. 100 (1991), no. 1, 87–109. MR 1124294, DOI 10.1016/0022-1236(91)90103-C
Anca Deliu and Björn Jawerth, Geometrical dimension versus smoothness, Constr. Approx. 8 (1992), no. 2, 211–222. MR 1152878, DOI 10.1007/BF01238270
[DoJ] D. Donoho and I. Johnstone, Minimax estimation via wavelet shrinkage, Stanford Univ. Tech. Report no. 402, Dept. of Statistics, 1992.
Charles Fefferman, Recent progress in classical Fourier analysis, Proceedings of the International Congress of Mathematicians (Vancouver, B.C., 1974) Canad. Math. Congress, Montreal, Que., 1975, pp. 95–118. MR 0510853
Michael Frazier and Björn Jawerth, A discrete transform and decompositions of distribution spaces, J. Funct. Anal. 93 (1990), no. 1, 34–170. MR 1070037, DOI 10.1016/0022-1236(90)90137-A
Michael Frazier, Björn Jawerth, and Guido Weiss, Littlewood-Paley theory and the study of function spaces, CBMS Regional Conference Series in Mathematics, vol. 79, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1991. MR 1107300, DOI 10.1090/cbms/079
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
P. I. Lizorkin, Operators connected with fractional differentiation, and classes of differentiable functions, Trudy Mat. Inst. Steklov. 117 (1972), 212–243, 345 (Russian). Studies in the theory of differentiable functions of several variables and its applications, IV. MR 0370166
[M1] Y. Meyer, Principe d'incertitude, bases Hilbertiennes et algèbres d'opérateurs, Séminaire Bourbaki 662 (1985-1986), 1-15.
Yves Meyer, Ondelettes et opérateurs. I, Actualités Mathématiques. [Current Mathematical Topics], Hermann, Paris, 1990 (French). Ondelettes. [Wavelets]. MR 1085487
Jaak Peetre, Sur les espaces de Besov, C. R. Acad. Sci. Paris Sér. A-B 264 (1967), A281–A283 (French). MR 218887
Jaak Peetre, New thoughts on Besov spaces, Duke University Mathematics Series, No. 1, Duke University, Mathematics Department, Durham, N.C., 1976. MR 0461123
Andreas Seeger, Remarks on singular convolution operators, Studia Math. 97 (1990), no. 2, 91–114. MR 1083340, DOI 10.4064/sm-97-2-91-114
E. M. Stein, On the functions of Littlewood-Paley, Lusin, and Marcinkiewicz, Trans. Amer. Math. Soc. 88 (1958), 430–466. MR 112932, DOI 10.1090/S0002-9947-1958-0112932-2
Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
E. M. Stein, The development of square functions in the work of A. Zygmund, Bull. Amer. Math. Soc. (N.S.) 7 (1982), no. 2, 359–376. MR 663787, DOI 10.1090/S0273-0979-1982-15040-6
Elias M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, vol. 43, Princeton University Press, Princeton, NJ, 1993. With the assistance of Timothy S. Murphy; Monographs in Harmonic Analysis, III. MR 1232192
[Ta] M. H. Taibleson, On the theory of Lipschitz spaces of distributions on Euclidean n-space. I, J. Math. Mech. 13 (1964), 407-480; II 14 (1965), 821-840; III 15 (1965), 973-981.
Hans Triebel, Spaces of distributions of Besov type on Euclidean $n$-space. Duality, interpolation, Ark. Mat. 11 (1973), 13–64. MR 348483, DOI 10.1007/BF02388506
H. Triebel, Interpolation theory, function spaces, differential operators, VEB Deutscher Verlag der Wissenschaften, Berlin, 1978. MR 500580
[Tr3] -, Theory of function spaces, Birkhäuser, Basel, 1983.
A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776
- [BGS]
- D. L. Burkholder, R. F. Gundy, and M. L. Silverstein, A maximal function characterization of the class , Trans. Amer. Math. Soc. 157 (1971), 137-153. MR 0274767 (43:527)
- [BS]
- A. Baernstein and E. Sawyer, Embedding and multiplier theorems for , Mem. Amer. Math. Soc., vol. 318, Amer. Math. Soc., Providence, RI, 1985. MR 776176 (86g:42036)
- [C]
- A. P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113-190. MR 0167830 (29:5097)
- [CMS]
- R. R. Coifman, Y. Meyer, and E. M. Stein, Some new function spaces and their applications to harmonic analysis, J. Funct. Anal. 62 (1985), 304-335. MR 791851 (86i:46029)
- [CW]
- F. M. Christ and M. I. Weinstein, Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation, J. Funct. Anal. 100 (1991), 87-109. MR 1124294 (92h:35203)
- [DeJ]
- A. Deliu and B. Jawerth, Geometrical dimension versus smoothness, Constr. Approx. 8 (1992), 211-222. MR 1152878 (93a:28008)
- [DoJ]
- D. Donoho and I. Johnstone, Minimax estimation via wavelet shrinkage, Stanford Univ. Tech. Report no. 402, Dept. of Statistics, 1992.
- [F]
- C. Fefferman, Recent progress in classical Fourier analysis, Proceedings of the International Congress of Mathematicians, Vancouver, Canad. Math. Congr., Vancouver, 1974, pp. 95-118. MR 0510853 (58:23308)
- [FJ]
- M. Frazier and B. Jawerth, A discrete transform and decompositions of distribution spaces, J. Funct. Anal. 93 (1990), 34-170. MR 1070037 (92a:46042)
- [FJW]
- M. Frazier, B. Jawerth, and G. Weiss, Littlewood-Paley theory and the study of function spaces, CBMS Regional Conf. Ser. in Math., vol. 79, Amer. Math. Soc., Providence, RI, 1991. MR 1107300 (92m:42021)
- [FS]
- C. Fefferman and E. M. Stein, spaces of several variables, Acta Math. 129 (1972), 137-193. MR 0447953 (56:6263)
- [L]
- P. I. Lizorkin, Operators connected with fractional derivatives and classes of differentiable functions, Trudy Mat. Inst. Steklov 117 (1972), 212-243. (Russian) MR 0370166 (51:6395)
- [M1]
- Y. Meyer, Principe d'incertitude, bases Hilbertiennes et algèbres d'opérateurs, Séminaire Bourbaki 662 (1985-1986), 1-15.
- [M2]
- -, Ondelettes et opérateurs, Hermann, Paris, 1990. MR 1085487 (93i:42002)
- [P1]
- J. Peetre, Sur les espaces de Besov, C. R. Acad. Sci. Paris Sér. I Math. 264 (1967), 281-283. MR 0218887 (36:1971)
- [P2]
- -, New thoughts on Besov spaces, Duke Univ. Math. Ser., vol. I, Durham, NC, 1976. MR 0461123 (57:1108)
- [Se]
- A. Seeger, Remarks on singular convolution operators, Studia Math. 97 (1990), 91-114. MR 1083340 (92a:42020)
- [St1]
- E. M. Stein, On the functions of Littlewood-Paley, Lusin and Marcinkiewicz, Trans. Amer. Math. Soc. 88 (1958), 430-466. MR 0112932 (22:3778)
- [St2]
- -, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, NJ, 1970. MR 0290095 (44:7280)
- [St3]
- -, The development of square functions in the work of A. Zygmund, Bull. Amer. Math. Soc. 7 (1982), 359-376. MR 663787 (83i:42001)
- [St4]
- -, Harmonic analysis: Real-variable methods, orthogonality, and oscillatory integrals, Princeton Univ. Press, Princeton, NJ, 1993. MR 1232192 (95c:42002)
- [Ta]
- M. H. Taibleson, On the theory of Lipschitz spaces of distributions on Euclidean n-space. I, J. Math. Mech. 13 (1964), 407-480; II 14 (1965), 821-840; III 15 (1965), 973-981.
- [Tr1]
- H. Triebel, Spaces of distributions of Besov type on Euclidean n-space: duality, interpolation, Ark. Mat. 11 (1973), 13-64. MR 0348483 (50:981)
- [Tr2]
- -, Interpolation theory, function spaces, differential operators, North-Holland, Amsterdam, 1978. MR 503903 (80i:46032b)
- [Tr3]
- -, Theory of function spaces, Birkhäuser, Basel, 1983.
- [Z]
- A. Zygmund, Trigonometric series, Cambridge Univ. Press, London, 1959. MR 0107776 (21:6498)
Review Information:
Reviewer:
Michael Frazier
Journal:
Bull. Amer. Math. Soc.
31 (1994), 119-125
DOI:
https://doi.org/10.1090/S0273-0979-1994-00498-7