Extensions of Fatou’s theorem to tangential asymptotic values
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- by T. K. Boehme and Max L. Weiss PDF
- Proc. Amer. Math. Soc. 27 (1971), 289-298 Request permission
Abstract:
Two theorems on the existence of tangential boundary values for harmonic functions on the disk are proved. One theorem is proved classically and the other is proved utilizing results concerning the maximal ideal space of ${H^\infty }$.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
- Lynn H. Loomis, The converse of the Fatou theorem for positive harmonic functions, Trans. Amer. Math. Soc. 53 (1943), 239–250. MR 7832, DOI 10.1090/S0002-9947-1943-0007832-1
- 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 M. Tsuji, On Fatou’s theorems on Poisson integrals, Japan J. Math. 15 (1938), 13-18.
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 27 (1971), 289-298
- MSC: Primary 31.10; Secondary 30.00
- DOI: https://doi.org/10.1090/S0002-9939-1971-0273039-9
- MathSciNet review: 0273039