Abstract
We consider the class of functions that are analytic in the domain G={z=x+iy:|z|<1, |y|>(−x)β for −1<x<0}, β>1, and satisfy the Hölder condition with exponent α in the closure Λ αa (G) of the domain G with interior cusps. As is proved, a nontangent set E condensed to the point O is an interpolation set for the pair of spaces Λ αa (G), Λαβ(E) if and only if the set E is sparse. Thus, an increase in smoothness occurs in the trace space. Bibliography: 5 titles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. M. Kotochigov and N. A. Shirokov, “Free interpolation in Hölder classes over Jordan domains,”J. Math. Sci.,80, No. 6, 2255–2275 (1996).
A. M. Kotochigov and N. A. Shirokov, “Interpolation near a cusp,”Algebra Anal. (1998) [to appear].
E. M. Dyn'kin, “Smooth functions on plane sets,”Dokl. Akad. Nauk SSSR,208, 25–27 (1973).
E. M. Dyn'kin, “Smoothness of Cauchy-type integrals,”Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova,92, 115–133 (1979).
K. Hoffman,Banach Spaces of Analytic Functions, Prentice-Hall, Englewood Cliffs, New Jersey (1962).
Additional information
Translated fromProblemy Matematicheskogo Analiza, No. 17, 1997, pp. 90–100.
Rights and permissions
About this article
Cite this article
Kotochigov, A.M. Interpolation in analytic Hölder classes in a neighborhood of an interior cusp. J Math Sci 97, 4238–4244 (1999). https://doi.org/10.1007/BF02365043
Issue Date:
DOI: https://doi.org/10.1007/BF02365043