Abstract
It is well known that every Hölder continuous function on the unit circle is the sum of two functions such that one of these functions extends holomorphically into the unit disc and the other extends holomorphically into the complement of the unit disc. We prove that an analogue of this holds for Hölder continuous functions on an annulus A which have zero averages on all circles contained in A which surround the hole.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Epstein, C. L. andKleiner, B., Spherical means in annular regions,Comm. Pure Appl. Math. 46 (1993), 441–451.
Globevnik, J., Zero integrals on circles and characterizations of harmonic and analytic functions,Trans. Amer. Math. Soc. 317 (1990), 313–330.
Globevnik, J., Holomorphic extensions from open families of circles,Trans. Amer. Math. Soc. 355 (2003), 1921–1931.
Muskhelishvili, N. I.,Singular Integral Equations, Noordhoff, Groningen, 1959.
Volchkov, V. V., Spherical means on Euclidean spaces.Ukraïn. Mat. Zh. 50 (1998), 1310–1315 (Russian). English transl.:Ukrainian Math. J. 50 (1998). 1496–1503.
Zygmund, A.,Trigonometric Series, Cambridge Univ. Press. 1959.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Globevnik, J. A decomposition of functions with zero means on circles. Ark. Mat. 43, 383–393 (2005). https://doi.org/10.1007/BF02384786
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02384786