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Equivalent definition of some weighted Hardy spaces

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Ukrainian Mathematical Journal Aims and scope

We present an equivalent definition of functions analytic in the half-plane ℂ+ = {z: Re z > 0} for which

$$ {\mathop {\sup }\limits_{{\left| \varphi \right|} < \frac{\pi } {2}} }{\left\{ {{\int\limits_0^{ + \infty } {{\left| {f{\left( {re^{{i\varphi }} } \right)}} \right|}^{\rho } e^{{ - \rho \sigma r{\left| {\sin \varphi } \right|}}} dr} }} \right\}} < + \infty . $$

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Authors and Affiliations

  1. Drohobych Pedagogic University, Drohobych, Ukraine

    V. M. Dil’nyi

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  1. V. M. Dil’nyi
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 9, pp. 1270–1274, September, 2008.

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Dil’nyi, V.M. Equivalent definition of some weighted Hardy spaces. Ukr Math J 60, 1477–1482 (2008). https://doi.org/10.1007/s11253-009-0140-1

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