One-sided boundary behavior for certain harmonic functions
HTML articles powered by AMS MathViewer
- by T. K. Boehme and Max L. Weiss PDF
- Proc. Amer. Math. Soc. 27 (1971), 280-288 Request permission
Abstract:
Some results concerning the maximal ideal space of ${H^\infty }$ of the disk are applied to harmonic functions. The methods yield a Lindelöf type theorem for harmonic functions and extend to bounded harmonic functions a criterion of Tanaka which is necessary and sufficient in order that the boundary value function be one-sided approximately continuous.References
- T. K. Boehme, M. Rosenfeld, and Max L. Weiss, Relations between bounded analytic functions and their boundary functions, J. London Math. Soc. (2) 1 (1969), 609–618. MR 249627, DOI 10.1112/jlms/s2-1.1.609
- 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
- Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0133008
- Kenneth Hoffman, Bounded analytic functions and Gleason parts, Ann. of Math. (2) 86 (1967), 74–111. MR 215102, DOI 10.2307/1970361
- M. Rosenfeld and Max L. Weiss, A function algebra approach to a theorem of Lindelöf, J. London Math. Soc. (2) 2 (1970), 209–215. MR 261360, DOI 10.1112/jlms/s2-2.2.209
- Chuji Tanaka, On the metric cluster values of the bounded regular function in the unit disk, Mem. School Sci. Engrg. Waseda Univ. 31 (1967), 119–129. MR 247101
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 27 (1971), 280-288
- MSC: Primary 30.85; Secondary 31.00
- DOI: https://doi.org/10.1090/S0002-9939-1971-0288293-7
- MathSciNet review: 0288293