Abstract
We prove sectorial extension theorems for ultraholomorphic function classes of Beurling type defined by weight functions with a controlled loss of regularity. The proofs are based on a reduction lemma, due to the second author, which allows to extract the Beurling from the Roumieu case, which was treated recently by Jiménez-Garrido, Sanz, and the third author. To have control on the opening of the sectors, where the extensions exist, we use the (mixed) growth index and the order of quasianalyticity of weight functions. As a consequence, we obtain corresponding extension results for classes defined by weight sequences. Additionally, we give information on the existence of continuous linear extension operators.
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Communicated by M. S. Moslehian.
AR was supported by FWF-Project P 32905-N, DNN and GS by FWF-Project P 33417-N.
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Nenning, D.N., Rainer, A. & Schindl, G. Ultraholomorphic sectorial extensions of Beurling type. Ann. Funct. Anal. 12, 45 (2021). https://doi.org/10.1007/s43034-021-00124-x
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DOI: https://doi.org/10.1007/s43034-021-00124-x
Keywords
- Ultraholomorphic function classes
- Extension results and extension operators
- Mixed setting
- Controlled loss of regularity
- Growth indices