Czechoslovak Mathematical Journal, Vol. 68, No. 2, pp. 387-414, 2018


A generalization to the Hardy-Sobolev spaces $H^{k,p}$ of an $L^p$-$L^1$ logarithmic type estimate

Imed Feki, Ameni Massoudi, Houda Nfata

Received September 6, 2016.   First published March 28, 2018.

Abstract:  The main purpose of this article is to give a generalization of the logarithmic-type estimate in the Hardy-Sobolev spaces $H^{k,p}(G)$; $k \in{\mathbb N}^*$, $1 \leq p \leq\infty$ and $G$ is the open unit disk or the annulus of the complex space $\mathbb C$.
Keywords:  annular domain; Poisson kernel; Hardy-Sobolev space; logarithmic estimate
Classification MSC:  30H10, 30C40, 35R30


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Affiliations:   Imed Feki, Ameni Massoudi, Laboratoire LAMHA-LR 11S52 Université de Sfax, Faculté des sciences de Sfax, Rue Jordanie, BP 1171, 3018 Sfax, Tunisie, e-mail: imed.feki@fss.rnu.tn; Houda Nfata, Laboratoire LAMHA-LR 11S52 Académie militaire, Al Funduq Al Jadid, Fondouk Jedid 8012, Tunisie


 
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