Geodesic
Pointwise inequalities of logarithmic type in Hardy-Hölder spaces
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 2, pp. 351-363.

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We prove some optimal logarithmic estimates in the Hardy space ${H}^{\infty }(G)$ with Hölder regularity, where $G$ is the open unit disk or an annular domain of $\mathbb {C}$. These estimates extend the results established by S. Chaabane and I. Feki in the Hardy-Sobolev space $H^{k,\infty }$ of the unit disk and those of I. Feki in the case of an annular domain. The proofs are based on a variant of Hardy-Landau-Littlewood inequality for Hölder functions. As an application of these estimates, we study the stability of both the Cauchy problem for the Laplace operator and the Robin inverse problem.
DOI : 10.1007/s10587-014-0106-9
Classification : 30C40, 30H05, 30H10
Keywords: Hardy-Sobolev space; Hardy-Landau-Littlewood inequality; Hölder regularity; Cauchy problem; inverse problem; logarithmic estimate 
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     title = {Pointwise inequalities of logarithmic type in {Hardy-H\"older} spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {351--363},
     publisher = {mathdoc},
     volume = {64},
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Chaabane, Slim; Feki, Imed. Pointwise inequalities of logarithmic type in Hardy-Hölder spaces. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 2, pp. 351-363. doi : 10.1007/s10587-014-0106-9. http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0106-9/

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