Pointwise inequalities of logarithmic type in Hardy-Hölder spaces

Slim Chaabane; Imed Feki

Czechoslovak Mathematical Journal (2014)

  • Volume: 64, Issue: 2, page 351-363
  • ISSN: 0011-4642

Abstract

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We prove some optimal logarithmic estimates in the Hardy space H ∞ ( G ) with Hölder regularity, where G is the open unit disk or an annular domain of ℂ . These estimates extend the results established by S. Chaabane and I. Feki in the Hardy-Sobolev space H k , ∞ 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.

How to cite

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Chaabane, Slim, and Feki, Imed. "Pointwise inequalities of logarithmic type in Hardy-Hölder spaces." Czechoslovak Mathematical Journal 64.2 (2014): 351-363. <http://eudml.org/doc/261978>.

@article{Chaabane2014,
abstract = {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.},
author = {Chaabane, Slim, Feki, Imed},
journal = {Czechoslovak Mathematical Journal},
keywords = {Hardy-Sobolev space; Hardy-Landau-Littlewood inequality; Hölder regularity; Cauchy problem; inverse problem; logarithmic estimate; Hardy-Sobolev space; Hardy-Landau-Littlewood inequality; Hölder regularity; Cauchy problem; inverse problem; logarithmic estimate},
language = {eng},
number = {2},
pages = {351-363},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Pointwise inequalities of logarithmic type in Hardy-Hölder spaces},
url = {http://eudml.org/doc/261978},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Chaabane, Slim
AU - Feki, Imed
TI - Pointwise inequalities of logarithmic type in Hardy-Hölder spaces
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 2
SP - 351
EP - 363
AB - 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.
LA - eng
KW - Hardy-Sobolev space; Hardy-Landau-Littlewood inequality; Hölder regularity; Cauchy problem; inverse problem; logarithmic estimate; Hardy-Sobolev space; Hardy-Landau-Littlewood inequality; Hölder regularity; Cauchy problem; inverse problem; logarithmic estimate
UR - http://eudml.org/doc/261978
ER -

References

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