Restricted principal values of bounded analytic and harmonic functions

Upadhyayula V. SATYANARAYANA; Max L. WEISS

doi:10.2969/jmsj/03310105

Upadhyayula V. SATYANARAYANA, Max L. WEISS

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JOURNAL FREE ACCESS

1981 Volume 33 Issue 1 Pages 105-123

DOI https://doi.org/10.2969/jmsj/03310105

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Published: 1981 Received: March 28, 1979 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) E. Bishop, Representing measures for points in a uniform algebra, Bull. Amer. Math. Soc., 70 (1964), 121-122.
2) T. K. Boehme, M. Rosenfeld and M. L. Weiss, Relations between bounded analytic functions and their boundary functions, J. London Math. Soc., (2) 1 (1969), 609-618.
3) T. K. Boehme and M. L. Weiss, One-sided boundary behavior for certain harmonic functions, Proc. Amer. Math. Soc., 27(2) (1971), 280-288.
4) L. Carleson, Interpolation by bounded analytic functions and the corona problem, Ann. of Math., (2) 76 (1962), 547-559.
5) J. L. Doob, The boundary values of analytic functions. II, Trans. Amer. Math. Soc., 35 (1933), 418-451.
6) J. L. Doob, One-sided cluster value theorems, Proc. London Math. Soc., (3) 13 (1963), 461-470.
7) T. W. Gamelin, Uniform Algebras, Prentice-Hall, Englewood Cliffs, New Jersey, 1969.
8) W. Gross, Zum Verhalten der konformen Abbildung am Rande, Math. Z., 3 (1919), 43-64.
9) K. Hoffman, Banach Spaces of Analytic Functions, Prentice-Hall, Englewood Cliffs, New Jersey, 1969.
10) K. Hoffman, Bounded analytic functions and Gleason parts, Ann. Math., 86 (1967), 74-111.
11) C. E. Rickart, General Theory of Banach Algebras, Van Nostrand, New York, 1960.
12) M. Rosenfeld and M. L. Weiss, A function algebra approach to a theorem of Lindelöf, J. London Math. Soc., (2) 2 (1970), 209-215.
13) U. V. Satyanarayana, The distribution of supports of representing measures for H^∞, in preparation.
14) U. V. Satyanarayana, Lindelöf-type theorems for bounded harmonic functions, in preparation.
15) M. L. Weiss, Cluster sets of bounded analytic functions from a Banach algebraic viewpoint, Ann. Acad. Sci. Fenn. Ser. A.I., no. 367 (1965), 14pp.

Right : [1] E. Bishop, Representing measures for points in a uniform algebra, Bull. Amer. Math. Soc., 70 (1964), 121-122.
[2] T. K. Boehme, M. Rosenfeld and M. L. Weiss, Relations between bounded analytic functions and their boundary functions, J. London Math. Soc., (2) 1 (1969), 609-618.
[3] T. K. Boehme and M. L. Weiss, One-sided boundary behavior for certain harmonic functions, Proc. Amer. Math. Soc., 27(2) (1971), 280-288.
[4] L. Carleson, Interpolation by bounded analytic functions and the corona problem, Ann. of Math., (2) 76 (1962), 547-559.
[5] J. L. Doob, The boundary values of analytic functions. II, Trans. Amer. Math. Soc., 35 (1933), 418-451.
[6] J. L. Doob, One-sided cluster value theorems, Proc. London Math. Soc., (3) 13 (1963), 461-470.
[7] T. W. Gamelin, Uniform Algebras, Prentice-Hall, Englewood Cliffs, New Jersey, 1969.
[8] W. Gross, Zum Verhalten der konformen Abbildung am Rande, Math. Z., 3 (1919), 43-64.
[9] K. Hoffman, Banach Spaces of Analytic Functions, Prentice-Hall, Englewood Cliffs, New Jersey, 1969.
[10] K. Hoffman, Bounded analytic functions and Gleason parts, Ann. Math., 86 (1967), 74-111.
[11] C. E. Rickart, General Theory of Banach Algebras, Van Nostrand, New York, 1960.
[12] M. Rosenfeld and M. L. Weiss, A function algebra approach to a theorem of Lindelöf, J. London Math. Soc., (2) 2 (1970), 209-215.
[13] U. V. Satyanarayana, The distribution of supports of representing measures for H^∞, in preparation.
[14] U. V. Satyanarayana, Lindelöf-type theorems for bounded harmonic functions, in preparation.
[15] M. L. Weiss, Cluster sets of bounded analytic functions from a Banach algebraic viewpoint, Ann. Acad. Sci. Fenn. Ser. A. I., no. 367 (1965), 14pp.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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