Abstract
LetU be an open set andb ∈ bdy(U). Let 0 < α< 1. Let A(U) denote the space of Lipα functions that are analytic onU, and a(U) the subspace lipα ∩ A(U). The space a(U ∪b), consisting of the functions that are analytic nearb, is dense in a(U). Letk be a natural number. We say that a(U) admits ak-th order continuous point derivation (cpd) atb if the functionalf → f(k) (b) is continuous on a(U ∪b), with respect to the Lipα norm.
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Supported by EOLAS grant BR/89/125.
Supported by EOLAS grant SC/90/070.
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Lord, D.J., O’Farrell, A.G. Boundary smoothness properties of Lipα analytic functions. J. Anal. Math. 63, 103–119 (1994). https://doi.org/10.1007/BF03008420
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DOI: https://doi.org/10.1007/BF03008420