Book Review
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MathSciNet review:
1567040
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Book Information:
Authors:
R. E. Edwards and
G. I. Gaudry
Title:
Littlewood-Paley and multiplier theory
Additional book information:
Springer-Verlag, Berlin, Heidelberg, New York, 1977, ix + 212 pp., $25.60.
D. G. Austin, A sample function property of martingales, Ann. Math. Statist. 37 (1966), 1396–1397. MR 198532, DOI 10.1214/aoms/1177699283
D. L. Burkholder, Martingale transforms, Ann. Math. Statist. 37 (1966), 1494–1504. MR 208647, DOI 10.1214/aoms/1177699141
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
4. A. P. Calderón, Commutators of singular integral operators, Amer. J. Math. 78 (1956), 310-320.
A.-P. Calderón, Algebras of singular integral operators, Singular Integrals (Proc. Sympos. Pure Math., Chicago, Ill., 1966) Amer. Math. Soc., Providence, R.I., 1967, pp. 18–55. MR 0394309
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
Ronald R. Coifman and Guido Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), no. 4, 569–645. MR 447954, DOI 10.1090/S0002-9904-1977-14325-5
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
Adriano M. Garsia, Martingale inequalities: Seminar notes on recent progress, Mathematics Lecture Note Series, W. A. Benjamin, Inc., Reading, Mass.-London-Amsterdam, 1973. MR 0448538
Stefan Kaczmarz, Über die Konvergenz der Reihen von Orthogonalfunktionen, Math. Z. 23 (1925), no. 1, 263–270 (German). MR 1544743, DOI 10.1007/BF01506233
11. J. E. Littlewood and R. E. A. C. Paley, Theorems on Fourier series and power series, J. London Math. Soc. 6 (1931), 230-233.
12. N. Lusin, Sur une propriété des fonctions à carré sommable, Bull. Calcutta Math. Soc. 20 (1930), 139-154.
J. Marcinkiewicz and A. Zygmund, A theorem of Lusin. Part I, Duke Math. J. 4 (1938), no. 3, 473–485. MR 1546069, DOI 10.1215/S0012-7094-38-00440-5
P. A. Meyer, Démonstration probabiliste de certaines inégalités de Littlewood-Paley. I. Les inégalités classiques, Séminaire de Probabilités, X (Première partie, Univ. Strasbourg, Strasbourg, année universitaire 1974/1975), Lecture Notes in Math., Vol. 511, Springer, Berlin, 1976, pp. 125–141 (French). MR 0501379
15. R. E. A. C. Paley, A remarkable series of orthogonal functions. I, Proc. London Math. Soc. 34 (1932), 241-264.
Gian-Carlo Rota, An “Alternierende Verfahren” for general positive operators, Bull. Amer. Math. Soc. 68 (1962), 95–102. MR 133847, DOI 10.1090/S0002-9904-1962-10737-X
D. C. Spencer, A function-theoretic identity, Amer. J. Math. 65 (1943), 147–160. MR 7437, DOI 10.2307/2371778
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 and Guido Weiss, On the theory of harmonic functions of several variables. I. The theory of $H^{p}$-spaces, Acta Math. 103 (1960), 25–62. MR 121579, DOI 10.1007/BF02546524
20. E. M. Stein, Classes H, C. R. Acad. Sci. Paris 263 (1966), 716-719.
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, Topics in harmonic analysis related to the Littlewood-Paley theory. , Annals of Mathematics Studies, No. 63, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1970. MR 0252961
Elias M. Stein, Maximal functions. I. Spherical means, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), no. 7, 2174–2175. MR 420116, DOI 10.1073/pnas.73.7.2174
24. M. H. Taibleson, On the theory of Lipschitz spaces of distributions on Euclidean n-spaces. I, J. Appl. Math. Mech. 13 (1964), 407-480; II (ibid) 14 (1965), 821-840.
M. H. Taibleson, Fourier analysis on local fields, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1975. MR 0487295
A. Zygmund, Une remarque sur un théorème de M. Kaczmarz, Math. Z. 25 (1926), no. 1, 297–298 (French). MR 1544811, DOI 10.1007/BF01283839
A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776
- 1.
- D. G. Austin, A sample property of martingales, Ann. Math. Statist. 37 (1966), 1396-1397. MR 0198532
- 2.
- D. L. Burkholder, Martingale transforms, Ann. Math. Statist. 37 (1966), 1494-1504. MR 208647
- 3.
- D. L. Burkholder, R. F. Gundy and M. L. Silverstein, A maximal function characterization of the class H, Trans. Amer. Math. Soc. 157 (1971), 137-153. MR 274767
- 4.
- A. P. Calderón, Commutators of singular integral operators, Amer. J. Math. 78 (1956), 310-320.
- 5.
- A. P. Calderón, Algebras of singular integral operators, Proc. Sympos. Pure Math. vol. 10, Amer. Math. Soc., Providence, R.I., 1967, pp. 18-55. MR 394309
- 6.
- A. P. Calderón, Cauchy integrals on Lipschitz curves and related operators, Proc. Nat. Acad. Sci. U.S.A. 74 (1977), 1324-1327. MR 466568
- 7.
- R. R. Coifman and Guido Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645. MR 447954
- 8.
- C. Fefferman and E. M. Stein, H, Acta Math. 129 (1972), 137-193. MR 447953
- 9.
- A. M. Garsia, Martingale inequalities, Benjamin, New York, 1973. MR 448538
- 10.
- S. Kaczmarz, Über die Konvergenz der Reihen von Orthogonalfunktionen, Math. Z. 23 (1925), 263-270. MR 1544743
- 11.
- J. E. Littlewood and R. E. A. C. Paley, Theorems on Fourier series and power series, J. London Math. Soc. 6 (1931), 230-233.
- 12.
- N. Lusin, Sur une propriété des fonctions à carré sommable, Bull. Calcutta Math. Soc. 20 (1930), 139-154.
- 13.
- J. Marcinkiewicz and A. Zygmund, A theorem of Lusin, Duke Math. J. 4 (1938), 473-485. MR 1546069
- 14.
- P.-A. Meyer, Démonstration probabiliste de certains inégalités de Littlewood-Paley, Exposés I and II, Lecture Notes in Math., vol. 511, Springer-Verlag, Berlin and New York, 1976, pp. 125-161. MR 501379
- 15.
- R. E. A. C. Paley, A remarkable series of orthogonal functions. I, Proc. London Math. Soc. 34 (1932), 241-264.
- 16.
- G. C. Rota, An "Alternieven de Verfahren" for general positive operators, Bull. Amer. Math. Soc. 68 (1962), 95-102. MR 133847
- 17.
- D. Spencer, A function theoretic identity, Amer. J. Math. 65 (1943), 147-160. MR 7437
- 18.
- E. M. Stein, On the functions of Littlewood-Paley, Lusin and Marcinkiewicz, Trans. Amer. Math. Soc. 88 (1958), 430-466. MR 112932
- 19.
- E. M. Stein and Guido Weiss, On the theory of harmonic functions of several variables, Acta Math. 103 (1960), 25-62. MR 121579
- 20.
- E. M. Stein, Classes H, C. R. Acad. Sci. Paris 263 (1966), 716-719.
- 21.
- E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, N.J., 1970. MR 290095
- 22.
- E. M. Stein, Topics in harmonic analysis related to the Littlewood-Paley theory, Ann. Math. Studies, no. 63, Princeton Univ. Press, Princeton, N.J., 1970. MR 252961
- 23.
- E. M. Stein, Maximal functions: Spherical means, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), 2174-2175. MR 420116
- 24.
- M. H. Taibleson, On the theory of Lipschitz spaces of distributions on Euclidean n-spaces. I, J. Appl. Math. Mech. 13 (1964), 407-480; II (ibid) 14 (1965), 821-840.
- 25.
- M. H. Taibleson, Fourier analysis on local fields, Math. Notes, no. 15, Princeton Univ. Press, Princeton, N.J., 1975. MR 487295
- 26.
- A. Zygmund, Une remarque sur un théorème de M. Kaczmarz, Math. Z. 25 (1926), 297-298. MR 1544811
- 27.
- A. Zygmund, Trigonometric series, Cambridge Univ. Press, New York, 1959. MR 107776
Review Information:
Reviewer:
R. R. Coifman
Reviewer:
Guido Weiss
Journal:
Bull. Amer. Math. Soc.
84 (1978), 242-250
DOI:
https://doi.org/10.1090/S0002-9904-1978-14464-4