Some Hölder-logarithmic estimates on Hardy-Sobolev spaces

Imed Feki; Ameni Massoudi

Czechoslovak Mathematical Journal (2024)

  • Volume: 74, Issue: 3, page 787-800
  • ISSN: 0011-4642

Abstract

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We prove some optimal estimates of Hölder-logarithmic type in the Hardy-Sobolev spaces H k , p ( G ) , where k ∈ ℕ * , 1 ≤ p ≤ ∞ and G is either the open unit disk 𝔻 or the annular domain G s , 0 < s < 1 of the complex space 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 ∂ 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.

How to cite

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Feki, Imed, and Massoudi, Ameni. "Some Hölder-logarithmic estimates on Hardy-Sobolev spaces." Czechoslovak Mathematical Journal 74.3 (2024): 787-800. <http://eudml.org/doc/299310>.

@article{Feki2024,
abstract = {We prove some optimal estimates of Hölder-logarithmic type in the Hardy-Sobolev spaces $H^\{k,p\}(G)$, where $k \in \{\mathbb \{N\}\}^*$, $1\le p\le \infty $ and $G$ is either the open unit disk $\{\mathbb \{D\}\}$ or the annular domain $G_s$, $0<s<1$ 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.},
author = {Feki, Imed, Massoudi, Ameni},
journal = {Czechoslovak Mathematical Journal},
keywords = {Hardy-Sobolev space; annular domain; Kernel function},
language = {eng},
number = {3},
pages = {787-800},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some Hölder-logarithmic estimates on Hardy-Sobolev spaces},
url = {http://eudml.org/doc/299310},
volume = {74},
year = {2024},
}

TY - JOUR
AU - Feki, Imed
AU - Massoudi, Ameni
TI - Some Hölder-logarithmic estimates on Hardy-Sobolev spaces
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 74
IS - 3
SP - 787
EP - 800
AB - We prove some optimal estimates of Hölder-logarithmic type in the Hardy-Sobolev spaces $H^{k,p}(G)$, where $k \in {\mathbb {N}}^*$, $1\le p\le \infty $ and $G$ is either the open unit disk ${\mathbb {D}}$ or the annular domain $G_s$, $0<s<1$ 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.
LA - eng
KW - Hardy-Sobolev space; annular domain; Kernel function
UR - http://eudml.org/doc/299310
ER -

References

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