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Book Review
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Book Information
Author(s):
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
References:
- [BGS]
- D. L. Burkholder, R. F. Gundy, and M. L. Silverstein, A maximal function characterization of the class $H^p$, Trans. Amer. Math. Soc. \textbf{157} (1971), 137--153.
- [BS]
- A. Baernstein and E. Sawyer, \emph{Embedding and multiplier theorems for $H^p(\Bbb R^n)$}, Amer. Math. Soc., Providence, RI, 1985.
- [C]
- A. P. Calder\'on, Intermediate spaces and interpolation, the complex method, Studia Math. \textbf{24} (1964), 113--190.
- [CMS]
- R. R. Coifman, Y. Meyer, and E. M. Stein, Some new function spaces and their applications to harmonic analysis, J. Funct. Anal. \textbf{62} (1985), 304--335.
- [CW]
- F. M. Christ and M. I. Weinstein, Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation, J. Funct. Anal. \textbf{100} (1991), 87--109.
- [DeJ]
- A. Deliu and B. Jawerth, Geometrical dimension versus smoothness, Constr. Approx. \textbf{8} (1992), 211--222.
- [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.
- [FJ]
- M. Frazier and B. Jawerth, A discrete transform and decompositions of distribution spaces, J. Funct. Anal. \textbf{93} (1990), 34--170.
- [FJW]
- M. Frazier, B. Jawerth, and G. Weiss, \emph{Littlewood-Paley theory and the study of function spaces}, Amer. Math. Soc., Providence, RI, 1991.
- [FS]
- C. Fefferman and E. M. Stein, $H^p$ spaces of several variables, Acta Math. \textbf{129} (1972), 137--193.
- [L]
- P. I. Lizorkin, Operators connected with fractional derivatives and classes of differentiable functions, Trudy Mat. Inst. Steklov \textbf{117} (1972), 212--243 \afterall (Russian).
- [M1]
- Y. Meyer, Principe d'incertitude, bases Hilbertiennes et alg\`ebres d'op\'erateurs, S\'eminaire Bourbaki \textbf{662} (1985--1986), 1--15.
- [M2]
- Y. Meyer, Ondelettes et op\'erateurs, Hermann, Paris, 1990.
- [P1]
- J. Peetre, Sur les espaces de Besov, C. R. Acad. Sci. Paris S\'er. I Math. \textbf{264} (1967), 281--283.
- [P2]
- J. Peetre, \emph{New thoughts on Besov spaces}, Durham, NC, 1976.
- [Se]
- A. Seeger, Remarks on singular convolution operators, Studia Math. \textbf{97} (1990), 91--114.
- [St1]
- E. M. Stein, On the functions of Littlewood-Paley, Lusin and Marcinkiewicz, Trans. Amer. Math. Soc. \textbf{88} (1958), 430--466.
- [St2]
- E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, NJ, 1970.
- [St3]
- E. M. Stein, The development of square functions in the work of A. Zygmund, Bull. Amer. Math. Soc. \textbf{7} (1982), 359--376.
- [St4]
- E. M. Stein, Harmonic analysis\,\RM : Real-variable methods, orthogonality, and oscillatory integrals, Princeton Univ. Press, Princeton, NJ, 1993.
- [Ta]
- M. H. Taibleson, On the theory of Lipschitz spaces of distributions on Euclidean $n$-space. \rm I, J. Math. Mech. \textbf{13} (1964), 407--480.
- [Tr1]
- H. Triebel, Spaces of distributions of Besov type on Euclidean $n$-space\,\RM : duality, interpolation, Ark. Mat. \textbf{11} (1973), 13--64.
- [Tr2]
- H. Triebel, Interpolation theory, function spaces, differential operators, North-Holland, Amsterdam, 1978.
- [Tr3]
- H. Triebel, Theory of function spaces, Birkh\"auser, Basel, 1983.
- [Z]
- A. Zygmund, Trigonometric series, Cambridge Univ. Press, London, 1959.
Additional Information:
Reviewer(s):
Michael
Frazier
Review Information:
Journal:
Bull. Amer. Math. Soc.
31
(1994),
119-125.
DOI:
10.1090/S0273-0979-1994-00498-7
PII:
S 0273-0979(1994)00498-7
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