Book Review
The AMS does not provide abstracts of book reviews.
You may download the entire review from the links below.
MathSciNet review:
1567400
Full text of review:
PDF
This review is available free of charge.
Book Information:
Author:
John B. Garnett
Title:
Bounded analytic functions
Additional book information:
Academic Press, New York, 1981, xvi + 468 pp., $59.00.
P. Fatou, Séries trigonométriques et séries de Taylor, Acta Math. 30 (1906), no. 1, 335–400 (French). MR 1555035, DOI 10.1007/BF02418579
2. F. Riesz and M. Riesz, Über die Randwerte einer analytischen Funktion, Comptes Rendus du 4. Congr. des Math. Scand. Stockholm (1916), 27-44.
Freidrich Riesz, Über die Randwerte einer analytischen Funktion, Math. Z. 18 (1923), no. 1, 87–95 (German). MR 1544621, DOI 10.1007/BF01192397
4. G. H. Hardy, The mean value of the modulus of an analytic function, Proc. London Math. Soc. 14(1915), 269-277.
5. M. Riesz, Les fonctions conjugées et les séries de Fourier, C. R. Acad. Sci. Paris Ser. A-B 178 (1924), 1464-1467.
6. A. N. Kolmogorov, Sur les fonctions harmonique et les séries de Fourier, Fund. Math. 7 (1925), 24-29.
G. H. Hardy and J. E. Littlewood, A maximal theorem with function-theoretic applications, Acta Math. 54 (1930), no. 1, 81–116. MR 1555303, DOI 10.1007/BF02547518
Arne Beurling, On two problems concerning linear transformations in Hilbert space, Acta Math. 81 (1948), 239–255. MR 27954, DOI 10.1007/BF02395019
Karel de Leeuw and Walter Rudin, Extreme points and extremum problems in $H_{1}$, Pacific J. Math. 8 (1958), 467–485. MR 98981
Walter Rudin, The closed ideals in an algebra of analytic functions, Canadian J. Math. 9 (1957), 426–434. MR 89254, DOI 10.4153/CJM-1957-050-0
Lennart Carleson, Interpolations by bounded analytic functions and the corona problem, Ann. of Math. (2) 76 (1962), 547–559. MR 141789, DOI 10.2307/1970375
12. E. Hille and J. D. Tamarkin, On the absolute integrability of Fourier transforms, Fund. Math. 25(1935), 329-352.
Henry Helson, Lectures on invariant subspaces, Academic Press, New York-London, 1964. MR 0171178
Béla Sz.-Nagy and Ciprian Foiaş, Harmonic analysis of operators on Hilbert space, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York; Akadémiai Kiadó, Budapest, 1970. Translated from the French and revised. MR 0275190
Peter D. Lax and Ralph S. Phillips, Scattering theory, Pure and Applied Mathematics, Vol. 26, Academic Press, New York-London, 1967. MR 0217440
Theodore W. Gamelin, Uniform algebras, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1969. MR 0410387
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 and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, No. 32, Princeton University Press, Princeton, N.J., 1971. MR 0304972
S. Bochner, Boundary values of analytic functions in several variables and of almost periodic functions, Ann. of Math. (2) 45 (1944), 708–722. MR 11132, DOI 10.2307/1969298
Henry Helson and David Lowdenslager, Prediction theory and Fourier series in several variables, Acta Math. 99 (1958), 165–202. MR 97688, DOI 10.1007/BF02392425
Donald Sarason, Invariant subspaces, Topics in operator theory, Math. Surveys, No. 13, Amer. Math. Soc., Providence, R.I., 1974, pp. 1–47. MR 0358396
Frank Forelli, Analytic measures, Pacific J. Math. 13 (1963), 571–578. MR 157193
Henry Helson, On a theorem of F. and M. Riesz, Colloq. Math. 3 (1955), 113–117. MR 69306, DOI 10.4064/cm-3-2-113-117
I. Glicksberg, The abstract F. and M. Riesz theorem, J. Functional Analysis 1 (1967), 109–122. MR 0211264, DOI 10.1016/0022-1236(67)90029-8
K. de Leeuw and I. Glicksberg, Quasi-invariance and analyticity of measures on compact groups, Acta Math. 109 (1963), 179–205. MR 144152, DOI 10.1007/BF02391812
Frank Forelli, Analytic and quasi-invariant measures, Acta Math. 118 (1967), 33–59. MR 209771, DOI 10.1007/BF02392475
Björn E. J. Dahlberg, Estimates of harmonic measure, Arch. Rational Mech. Anal. 65 (1977), no. 3, 275–288. MR 466593, DOI 10.1007/BF00280445
Lennart Carleson, An interpolation problem for bounded analytic functions, Amer. J. Math. 80 (1958), 921–930. MR 117349, DOI 10.2307/2372840
Lars Hörmander, Generators for some rings of analytic functions, Bull. Amer. Math. Soc. 73 (1967), 943–949. MR 226387, DOI 10.1090/S0002-9904-1967-11860-3
Charles Fefferman, Characterizations of bounded mean oscillation, Bull. Amer. Math. Soc. 77 (1971), 587–588. MR 280994, DOI 10.1090/S0002-9904-1971-12763-5
Paul Koosis, Introduction to $H_{p}$ spaces, London Mathematical Society Lecture Note Series, vol. 40, Cambridge University Press, Cambridge-New York, 1980. With an appendix on Wolff’s proof of the corona theorem. MR 565451
- 1.
- P. Fatou, Séries trigonométriques et séries de Taylor, Acta Math. 30 (1906), 335-400. MR 1555035
- 2.
- F. Riesz and M. Riesz, Über die Randwerte einer analytischen Funktion, Comptes Rendus du 4. Congr. des Math. Scand. Stockholm (1916), 27-44.
- 3.
- F. Riesz, Über die Randwerte einer analytischen Funktion, Math. Z. 18 (1923), 87-95. MR 1544621
- 4.
- G. H. Hardy, The mean value of the modulus of an analytic function, Proc. London Math. Soc. 14(1915), 269-277.
- 5.
- M. Riesz, Les fonctions conjugées et les séries de Fourier, C. R. Acad. Sci. Paris Ser. A-B 178 (1924), 1464-1467.
- 6.
- A. N. Kolmogorov, Sur les fonctions harmonique et les séries de Fourier, Fund. Math. 7 (1925), 24-29.
- 7.
- G. H. Hardy and J. E. Littlewood, A maximal theorem with function theoretic applications, Acta Math. 54 (1930), 81-116. MR 1555303
- 8.
- A. Beurling, On two problems concerning linear transformations in Hilbert space, Acta Math. 81 (1949), 239-255. MR 27954
- 9.
- K. deLeeuw and W. Rudin, Extreme points and extremum problems in H1, Pacific J. Math. 8 (1958), 467-485. MR 98981
- 10.
- W. Rudin, The closed ideals in an algebra of analytic functions, Canad. J. Math. 9 (1957), 426-434. MR 89254
- 11.
- L. Carleson, Interpolations by bounded analytic functions and the corona problem, Ann. of Math. (2) 76 (1962), 547-559. MR 141789
- 12.
- E. Hille and J. D. Tamarkin, On the absolute integrability of Fourier transforms, Fund. Math. 25(1935), 329-352.
- 13.
- H. Helson, Lectures on invariant subspaces, Academic Press, New York and London, 1964. MR 171178
- 14.
- B. Sz. -Nagy and C. Foiaş, Harmonic analysis of operators on Hilbert space, North-Holland, Amsterdam, 1970. MR 275190
- 15.
- P. D. Lax and R. S. Phillips, Scattering theory, Academic Press, New York and London, 1967. MR 217440
- 16.
- T. W. Gamelin, Uniform algebras, Prentice-Hall, Englewood-Cliffs, N. J., 1969. MR 410387
- 17.
- E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, N. J., 1970. MR 290095
- 18.
- E. M. Stein and G. Weiss, Fourier analysis on Euclidean spaces, Princeton Univ. Press, Princeton, N. J., 1971. MR 304972
- 19.
- S. Bochner, Boundary values of analytic functions in several variables and of almost periodic functions, Ann. of Math. (2) 45 (1944), 708-722. MR 11132
- 20.
- H. Helson and D. Lowderslager, Prediction theory and Fourier series in several variables, Acta Math. 99(1958), 165-201. MR 97688
- 21.
- D. Sarason, Invariant subspaces, Topics in Operator Theory, Math. Surveys, No. 13, Amer. Math. Soc. Providence, R. I., 1974, pp. 1-47. MR 358396
- 22.
- F. Forelli, Analytic measures, Pacific J. Math. 13 (1963), 571-578. MR 157193
- 23.
- H. Helson, On a theorem of F. and M. Riesz, Colloq. Math. 3 (1955), 113-117. MR 69306
- 24.
- I. Glicksberg, The abstract F. and M. Riesz theorem, J. Funct. Anal. 1 (1967), 109-122. MR 211264
- 25.
- K. deLeeuw and I. Glicksberg, Quasi-invariance and analyticity of measures on compact groups, Acta Math. 109 (1963), 179-205. MR 144152
- 26.
- F. Forelli, Analytic and quasi-invariant measures, Acta Math. 118 (1967), 33-59. MR 209771
- 27.
- B. Dahlberg, Estimates of harmonic measure, Arch. Rational Mech. 65 (1977), 272-288. MR 466593
- 28.
- L. Carleson, An interpolation problem for bounded analytic functions, Amer. J. Math. 80 (1958), 921-930. MR 117349
- 29.
- L. Hörmander, Generators for some rings of analytic functions, Bull. Amer. Math. Soc. 73 (1967), 943-949. MR 226387
- 30.
- C. Fefferman, Characterizations of bounded mean oscillation, Bull. Amer. Math. Soc. 77 (1971), 587-588. MR 280994
- 31.
- P. Koosis, Introduction to H, Cambridge Univ. Press, Cambridge, 1980. MR 565451
Review Information:
Reviewer:
Donald E. Sarason
Journal:
Bull. Amer. Math. Soc.
8 (1983), 102-108
DOI:
https://doi.org/10.1090/S0273-0979-1983-15097-8