## Asymptotic values of modulus $1$ of functions in the unit ball of $H^{\infty }$

HTML articles powered by AMS MathViewer

- by Kar Koi Leung PDF
- Trans. Amer. Math. Soc.
**203**(1975), 119-128 Request permission

## Abstract:

The main purpose of this paper is to prove a theorem concerning a necessary and sufficient condition for an inner function to have a limiting value of modulus 1 along an arc inside the unit disc, terminating at a point of the unit circle.## References

- P. R. Ahern and D. N. Clark,
*Radial $n\textrm {th}$ derivatives of Blaschke products*, Math. Scand.**28**(1971), 189â201. MR**318495**, DOI 10.7146/math.scand.a-11015
C. CarathĂ©odory, - G. T. Cargo,
*Angular and tangential limits of Blaschke products and their successive derivatives*, Canadian J. Math.**14**(1962), 334â348. MR**136743**, DOI 10.4153/CJM-1962-026-2 - E. F. Collingwood and A. J. Lohwater,
*The theory of cluster sets*, Cambridge Tracts in Mathematics and Mathematical Physics, No. 56, Cambridge University Press, Cambridge, 1966. MR**0231999**, DOI 10.1017/CBO9780511566134 - Otto Frostman,
*Sur les produits de Blaschke*, Kungl. Fysiografiska SĂ€llskapets i Lund FĂ¶rhandlingar [Proc. Roy. Physiog. Soc. Lund]**12**(1942), no.Â 15, 169â182 (French). MR**12127** - K. K. Leung and C. N. Linden,
*Asymptotic values of modulus $1$ of Blaschke products*, Trans. Amer. Math. Soc.**203**(1975), 107â118. MR**361084**, DOI 10.1090/S0002-9947-1975-0361084-2 - David Protas,
*Tangential limits of Blaschke products and functions of bounded characteristic*, Arch. Math. (Basel)**22**(1971), 631â641. MR**299798**, DOI 10.1007/BF01222628 - E. C. Titchmarsh,
*Han-shu lun*, Science Press, Peking, 1964 (Chinese). Translated from the English by Wu Chin. MR**0197687**

*Funktionentheorie*. Band 2, BirkhĂ€user, Basel, 1950; English transl.,

*Theory of functions of a complex variable*. Vol. 2, Chelsea, New York, 1954. MR

**12**, 248;

**16**, 346.

## Additional Information

- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**203**(1975), 119-128 - MSC: Primary 30A72; Secondary 30A76
- DOI: https://doi.org/10.1090/S0002-9947-1975-0361085-4
- MathSciNet review: 0361085