Book Review
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MathSciNet review:
1568176
Full text of review:
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Book Information:
Author:
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.
A.-P. Calderón, Cauchy integrals on Lipschitz curves and related operators, Proc. Nat. Acad. Sci. U.S.A. 74 (1977), no. 4, 1324–1327. MR 466568, DOI 10.1073/pnas.74.4.1324
R. R. Coifman, A. McIntosh, and Y. Meyer, L’intégrale de Cauchy définit un opérateur borné sur $L^{2}$ pour les courbes lipschitziennes, Ann. of Math. (2) 116 (1982), no. 2, 361–387 (French). MR 672839, DOI 10.2307/2007065
Guy David, Opérateurs intégraux singuliers sur certaines courbes du plan complexe, Ann. Sci. École Norm. Sup. (4) 17 (1984), no. 1, 157–189 (French). MR 744071
Guy David, Opérateurs d’intégrale singulière sur les surfaces régulières, Ann. Sci. École Norm. Sup. (4) 21 (1988), no. 2, 225–258 (French). MR 956767
[DS] G. David and S. Semmes, Singular integrals and rectifiable sets in : au-delà des graphes lipschitziens, Astérisque 193 (1991), 1-145.
José R. Dorronsoro, A characterization of potential spaces, Proc. Amer. Math. Soc. 95 (1985), no. 1, 21–31. MR 796440, DOI 10.1090/S0002-9939-1985-0796440-3
K. J. Falconer, The geometry of fractal sets, Cambridge Tracts in Mathematics, vol. 85, Cambridge University Press, Cambridge, 1986. MR 867284
Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York, Inc., New York, 1969. MR 0257325
Peter W. Jones, Rectifiable sets and the traveling salesman problem, Invent. Math. 102 (1990), no. 1, 1–15. MR 1069238, DOI 10.1007/BF01233418
Pertti Mattila, Geometry of sets and measures in Euclidean spaces, Cambridge Studies in Advanced Mathematics, vol. 44, Cambridge University Press, Cambridge, 1995. Fractals and rectifiability. MR 1333890, DOI 10.1017/CBO9780511623813
Stephen W. Semmes, A criterion for the boundedness of singular integrals on hypersurfaces, Trans. Amer. Math. Soc. 311 (1989), no. 2, 501–513. MR 948198, DOI 10.1090/S0002-9947-1989-0948198-0
Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
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
- [C]
- A. P. Calderón, Cauchy integrals on Lipschitz curves and related operators, Proc. Nat. Acad. Sci. U.S.A. 74 (1977), 1324-1327. MR 0466568 (57:6445)
- [CMM]
- R. R. Coifman, A. McIntosh and Y. Meyer, L'intégrale de Cauchy définit un opérateur borné sur pour les courbes lipschitziennes, Ann. of Math. (2) 116 (1982), 361-388. MR 672839 (84m:42027)
- [D1]
- G. David, Opérateurs integraux singuliers sur certaines courbes du plan complexe, Ann. Sci. École Norm. Sup. (4) 17 (1984), 157-189. MR 744071 (85k:42026)
- [D2]
- -, Opérateurs d'integrale singuliere sur les surfaces régulières, Ann. Sci. École Norm. Sup. (4) 21 (1988), 225-258. MR 956767 (89m:42014)
- [DS]
- G. David and S. Semmes, Singular integrals and rectifiable sets in : au-delà des graphes lipschitziens, Astérisque 193 (1991), 1-145.
- [D]
- J. R. Dorronsoro, A characterization of potential spaces, Proc. Amer. Math. Soc. 95 (1985), 21-31. MR 796440 (86k:46046)
- [F]
- K. J. Falconer, Geometry of fractal sets, Cambridge Univ. Press, Cambridge, 1985. MR 867284 (88d:28001)
- [Fe]
- H. Federer, Geometric measure theory, Springer-Verlag, Berlin and New York, 1969. MR 0257325 (41:1976)
- [J]
- P. W. Jones, Rectifiable sets and the traveling salesman problem, Invent. Math. 102 (1990), 1-15. MR 1069238 (91i:26016)
- [M]
- P. Mattila, Geometry of sets and measures in Euclidean spaces, Cambridge Univ. Press, Cambridge, 1995 (to appear). MR 1333890 (96h:28006)
- [S]
- S. Semmes, A criterion for the boundedness of singular integrals on hypersurfaces, Trans. Amer. Math. Soc. 311 (1989), 501-513. MR 948198 (89k:42017)
- [S1]
- E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, NJ, 1970. MR 0290095 (44:7280)
- [S2]
- -, Harmonic analysis: Real-variable methods, orthogonality, and oscillatory integrals, Princeton Univ. Press, Princeton, NJ, 1993. MR 1232192 (95c:42002)
Review Information:
Reviewer:
Pertti Mattila
Journal:
Bull. Amer. Math. Soc.
32 (1995), 322-325
DOI:
https://doi.org/10.1090/S0273-0979-1995-00588-4