We use a Hölder condition with respect to a variable exponent Lebesgue norm to introduce classes of analytic functions in a disc and of holomorphic functions in a ball. We describe outer functions in the disc and find the smoothness decay of a function in comparison with the smoothness of its modulus on the boundary, in the case of the disc and of the ball.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 480, 2019, pp. 206–213.
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Shirokov, N.A. Outer Functions in Classes of Analytic Functions of Variable Smoothness. J Math Sci 251, 296–300 (2020). https://doi.org/10.1007/s10958-020-05091-7
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DOI: https://doi.org/10.1007/s10958-020-05091-7