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Book Review
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Book Information
Author(s):
Guy David and Stephen Semmes
Title:
Analysis of and on uniformly rectifiable sets
Additional book information:
Math Surveys Monographs, vol. 38, Amer. Math. Soc., Providence, RI, 1993, xii + 356 pp., US$98.00. ISBN 0-8218-1537-7
References:
- [C]
- A. P. Calder\'on, Cauchy integrals on Lipschitz curves and related operators, Proc. Nat. Acad. Sci. U.S.A. \textbf{74} (1977), 1324--1327.
- [CMM]
- R. R. Coifman, A. McIntosh and Y. Meyer, L{\rm '}int\'egrale de Cauchy d\'efinit un op\'erateur born\'e sur $L^2$ pour les courbes lipschitziennes, Ann. of Math. (2) \textbf{116} (1982), 361--388.
- [D1]
- G. David, Op\'erateurs integraux singuliers sur certaines courbes du plan complexe, Ann. Sci. \'Ecole Norm. Sup. (4) \textbf{17} (1984), 157--189.
- [D2]
- G. David, Op\'erateurs d\,{\rm '}integrale singuliere sur les surfaces r\'eguli\`eres, Ann. Sci. \'Ecole Norm. Sup. (4) \textbf{21} (1988), 225--258.
- [DS]
- G. David and S. Semmes, Singular integrals and rectifiable sets in $\Bbb R^n${\rm :} au-del\`a des graphes lipschitziens, Ast\'erisque \textbf{193} (1991), 1--145.
- [D]
- J. R. Dorronsoro, A characterization of potential spaces, Proc. Amer. Math. Soc. \textbf{95} (1985), 21--31.
- [F]
- K. J. Falconer, Geometry of fractal sets, Cambridge Univ. Press, Cambridge, 1985.
- [Fe]
- H. Federer, Geometric measure theory, Springer-Verlag, Berlin and New York, 1969.
- [J]
- P. W. Jones, Rectifiable sets and the traveling salesman problem, Invent. Math. \textbf{102} (1990), 1--15.
- [M]
- P. Mattila, Geometry of sets and measures in Euclidean spaces, Cambridge Univ. Press, Cambridge, 1995.
- [S]
- S. Semmes, A criterion for the boundedness of singular integrals on hypersurfaces, Trans. Amer. Math. Soc. \textbf{311} (1989), 501--513.
- [S1]
- E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, NJ, 1970.
- [S2]
- E. M. Stein, Harmonic analysis\,{\rm :} Real-variable methods, orthogonality, and oscillatory integrals, Princeton Univ. Press, Princeton, NJ, 1993.
Additional Information:
Reviewer(s):
Pertti
Mattila
Review Information:
Journal:
Bull. Amer. Math. Soc.
32
(1995),
322-325.
DOI:
10.1090/S0273-0979-1995-00588-4
PII:
S 0273-0979(1995)00588-4
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