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Book Review

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Book Information:

Author: Antoni Zygmund
Title: Trigonometric series, Vols. I, II
Additional book information: third edition, with a foreword by Robert Fefferman, Cambridge Mathematical Library, Cambridge University Press, 2002, (Vol. I) xiv + 383 pp., (Vol. II) viii + 364, ISBN 0-521-89053-5, $60.00$

Antoni Zygmund, Selected papers of Antoni Zygmund. Vol. 1, Mathematics and its Applications (East European Series), vol. 41/1, Kluwer Academic Publishers Group, Dordrecht, 1989. Edited by A. Hulanicki, P. Wojtaszczyk and W. Żelazko. MR 1112134

G. H. Hardy, Collected papers of G. H. Hardy (including joint papers with J. E. Littlewood and others). Vol. III, Clarendon Press, Oxford, 1969. Edited by a committee appointed by the London Mathematical Society. MR 0255362

L.-Ȧ. Lindahl and F. Poulsen (eds.), Thin sets in harmonic analysis, Lecture Notes in Pure and Applied Mathematics, Vol. 2, Marcel Dekker, Inc., New York, 1971. Seminars held at Institute Mittag-Leffler, Univ. Stockholm, Stockholm, 1969–1970. MR 0393993

Wiesław Żelazko (ed.), Fourier analysis and related topics, Banach Center Publications, vol. 56, Polish Academy of Sciences, Institute of Mathematics, Warsaw, 2002. Papers from the International Symposium held in Będlewo, October 15–21, 2000. MR 1971559

Colin C. Graham and O. Carruth McGehee, Essays in commutative harmonic analysis, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 238, Springer-Verlag, New York-Berlin, 1979. MR 550606

Henry Helson, Harmonic analysis, Addison-Wesley Publishing Company, Advanced Book Program, Reading, MA, 1983. MR 729682

Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I: Structure of topological groups. Integration theory, group representations, Die Grundlehren der mathematischen Wissenschaften, Band 115, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963. MR 0156915

Jean-Pierre Kahane, Séries de Fourier absolument convergentes, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 50, Springer-Verlag, Berlin-New York, 1970 (French). MR 0275043

Jean-Pierre Kahane and Raphaël Salem, Ensembles parfaits et séries trigonométriques, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1301, Hermann, Paris, 1963 (French). MR 0160065

Yitzhak Katznelson, An introduction to harmonic analysis, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0248482

Jorge M. López and Kenneth A. Ross, Sidon sets, Lecture Notes in Pure and Applied Mathematics, Vol. 13, Marcel Dekker, Inc., New York, 1975. MR 0440298

Michael B. Marcus and Gilles Pisier, Random Fourier series with applications to harmonic analysis, Annals of Mathematics Studies, No. 101, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1981. MR 630532

Yves Meyer, Algebraic numbers and harmonic analysis, North-Holland Mathematical Library, Vol. 2, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1972. MR 0485769

Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0152834

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

Elias M. Stein and Rami Shakarchi, Fourier analysis, Princeton Lectures in Analysis, vol. 1, Princeton University Press, Princeton, NJ, 2003. An introduction. MR 1970295

N. Yu. Antonov, Convergence of Fourier series, Proceedings of the XX Workshop on Function Theory (Moscow, 1995), 1996, pp. 187–196. MR 1407066

J. Marshall Ash and Gang Wang, A survey of uniqueness questions in multiple trigonometric series, Harmonic analysis and nonlinear differential equations (Riverside, CA, 1995) Contemp. Math., vol. 208, Amer. Math. Soc., Providence, RI, 1997, pp. 35–71. MR 1467001, DOI 10.1090/conm/208/02734

J. Marshall Ash and Gang Wang, Some spherical uniqueness theorems for multiple trigonometric series, Ann. of Math. (2) 151 (2000), no. 1, 1–33. MR 1745020, DOI 10.2307/121110

20.

S.V. BOCHKAREV. Everywhere divergent Fourier-Walsh series. Doklady Mathematics 67 n $^{\circ}$ 3 (2003), 307-310.

Jean Bourgain, Sidon sets and Riesz products, Ann. Inst. Fourier (Grenoble) 35 (1985), no. 1, 137–148. MR 781783

Lennart Carleson, On convergence and growth of partial sums of Fourier series, Acta Math. 116 (1966), 135–157. MR 199631, DOI 10.1007/BF02392815

Stéphane Jaffard and Yves Meyer, Wavelet methods for pointwise regularity and local oscillations of functions, Mem. Amer. Math. Soc. 123 (1996), no. 587, x+110. MR 1342019, DOI 10.1090/memo/0587

S. V. Konyagin, On the divergence everywhere of trigonometric Fourier series, Mat. Sb. 191 (2000), no. 1, 103–126 (Russian, with Russian summary); English transl., Sb. Math. 191 (2000), no. 1-2, 97–120. MR 1753494, DOI 10.1070/SM2000v191n01ABEH000449

25.

H. LEBESGUE. Sur les intégrales singulières. Annales de la Faculté des Sciences de Toulouse (3) 1 (1909), 25-117.

26.

R. SALEM. Review: Trigonometric series (A. Zygmund), Bulletin American Mathematical Society 66 (1960), 6-12.

Review Information:

Reviewer: Jean-Pierre Kahane
Affiliation: Université Paris-Sud
Email: jean-pierre.kahane@math.u-psud.fr