Geodesic
Pointwise inequalities of logarithmic type in Hardy-Hölder spaces
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 2, pp. 351-363 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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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     author = {Chaabane, Slim and Feki, Imed},
     title = {Pointwise inequalities of logarithmic type in {Hardy-H\"older} spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {351--363},
     year = {2014},
     volume = {64},
     number = {2},
     doi = {10.1007/s10587-014-0106-9},
     mrnumber = {3277741},
     zbl = {06391499},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0106-9/}
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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

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