Abstract
We introduce and characterize two types of interpolating sequences in the unit disc \(\mathbb {D}\) of the complex plane for the class of all functions being the product of two analytic functions in \(\mathbb {D}\), one bounded and another regular up to the boundary of \(\mathbb {D}\), concretely in the Lipschitz class, and at least one of them vanishing at some point of \(\overline {\mathbb {D}}\).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bruna J, Nicolau A and Øyma K, A note on interpolation in the Hardy spaces of the unit disc, Proc. Amer. Math. Soc. 124 (1996) 1197–1204
Carleson L, An interpolation problem for bounded analytic functions, Amer. J. Math. 80 (1958) 921–930
Kotochigov A M, Free interpolation in the spaces of analytic functions with derivative of order s from the Hardy space, J. Math. Sci. (N. Y.) 129 (2005) 4022–4039
Kronstadt E P, Interpolating sequences for functions satisfying a Lipschitz condition, Pacific. J. Math. 63 (1976) 169–177
Vasyunin V I, Characterization of finite unions of Carleson sets in terms of solvability of interpolation problems. (Russian) Investigations on linear operators and the theory of functions, XIII. Zap. Nauchn. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 135 (1984) 31–35
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
TUGORES, F., TUGORES, L. Interpolation for a subclass of H ∞ . Proc Math Sci 124, 343–348 (2014). https://doi.org/10.1007/s12044-014-0181-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12044-014-0181-8