Pointwise inequalities of logarithmic type in Hardy-Hölder spaces

Chaabane, Slim   ; Feki, Imed

Czechoslovak Mathematical Journal, Tome 64 (2014) no. 2, pp. 351-363

Abstract (VO)

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.

Détail

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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