Geodesic
Some Hölder-logarithmic estimates on Hardy-Sobolev spaces
Czechoslovak Mathematical Journal, Tome 74 (2024) no. 3, pp. 787-800 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We prove some optimal estimates of Hölder-logarithmic type in the Hardy-Sobolev spaces $H^{k,p}(G)$, where $k \in {\mathbb N}^*$, $1\leq p\leq \infty $ and $G$ is either the open unit disk ${\mathbb D}$ or the annular domain $G_s$, $0$ of the complex space ${\mathbb C}$. More precisely, we study the behavior on the interior of $G$ of any function $f$ belonging to the unit ball of the Hardy-Sobolev spaces $H^{k,p}(G)$ from its behavior on any open connected subset $I$ of the boundary $\partial G$ of $G$ with respect to the $L^1$-norm. Our results can be viewed as an improvement and generalization of those established in S. Chaabane, I. Feki (2009), I. Feki, H. Nfata, F. Wielonsky (2012), I. Feki (2013), I. Feki, H. Nfata (2014). As an application, we establish a logarithmic stability results for the Cauchy problem of the identification of Robin's coefficient by boundary measurements.
We prove some optimal estimates of Hölder-logarithmic type in the Hardy-Sobolev spaces $H^{k,p}(G)$, where $k \in {\mathbb N}^*$, $1\leq p\leq \infty $ and $G$ is either the open unit disk ${\mathbb D}$ or the annular domain $G_s$, $0$ of the complex space ${\mathbb C}$. More precisely, we study the behavior on the interior of $G$ of any function $f$ belonging to the unit ball of the Hardy-Sobolev spaces $H^{k,p}(G)$ from its behavior on any open connected subset $I$ of the boundary $\partial G$ of $G$ with respect to the $L^1$-norm. Our results can be viewed as an improvement and generalization of those established in S. Chaabane, I. Feki (2009), I. Feki, H. Nfata, F. Wielonsky (2012), I. Feki (2013), I. Feki, H. Nfata (2014). As an application, we establish a logarithmic stability results for the Cauchy problem of the identification of Robin's coefficient by boundary measurements.
DOI : 10.21136/CMJ.2024.0552-23
Classification : 30C40, 30H05, 30H10, 35R30
Keywords: Hardy-Sobolev space; annular domain; Kernel function 
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     title = {Some {H\"older-logarithmic} estimates on {Hardy-Sobolev} spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {787--800},
     year = {2024},
     volume = {74},
     number = {3},
     doi = {10.21136/CMJ.2024.0552-23},
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Feki, Imed; Massoudi, Ameni. Some Hölder-logarithmic estimates on Hardy-Sobolev spaces. Czechoslovak Mathematical Journal, Tome 74 (2024) no. 3, pp. 787-800. doi: 10.21136/CMJ.2024.0552-23

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