Some Hardy-type estimates in realized homogeneous Besov and Triebel–Lizorkin spaces

Madani Moussai

doi:10.5802/afst.1622

Madani Moussai ¹

¹ Laboratory of Functional Analysis and Geometry of Spaces, Mohamed Boudiaf University of M’Sila, 28000 M’Sila (Algeria)

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 1, pp. 39-55.

Résumé
Abstract

Nous monterons que les espaces homogènes réalisés de Besov $\dot{\tilde{B}}_{p_{0}, p}^{s_{0}} (ℝ)$ et de Triebel–Lizorkin $\dot{\tilde{F}}_{p_{0}, p}^{s_{0}} (ℝ)$ s’injectent continûment dans les espaces quasi-Banach de Lebesgue à poids $L_{p} {(ℝ; | x |}^{- p (s_{0} - n / p_{0} + n / p)} d x)$ pour $p_{0} < p$ et ${(n / p_{0} - n)}_{+} < s_{0} < n / p_{0}$ .

We prove that the realized homogeneous Besov $\dot{\tilde{B}}_{p_{0}, p}^{s_{0}} (ℝ)$ and Triebel–Lizorkin $\dot{\tilde{F}}_{p_{0}, p}^{s_{0}} (ℝ)$ spaces are continuously embedded in the quasi-Banach weighted Lebesgue spaces $L_{p} {(ℝ; | x |}^{- p (s_{0} - n / p_{0} + n / p)} d x)$ for $p_{0} < p$ and ${(n / p_{0} - n)}_{+} < s_{0} < n / p_{0}$ .

Reçu le : 2017-12-09
Accepté le : 2017-12-19
Publié le : 2020-07-24

DOI : 10.5802/afst.1622

Classification : 46E35
Mots clés : Homogeneous Besov spaces, homogeneous Triebel–Lizorkin spaces, realizations

Affiliations des auteurs :

Madani Moussai ¹

¹ Laboratory of Functional Analysis and Geometry of Spaces, Mohamed Boudiaf University of M’Sila, 28000 M’Sila (Algeria)

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Some {Hardy-type} estimates in realized homogeneous {Besov} and {Triebel{\textendash}Lizorkin} spaces},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {39--55},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
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     doi = {10.5802/afst.1622},
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Madani Moussai. Some Hardy-type estimates in realized homogeneous Besov and Triebel–Lizorkin spaces. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 1, pp. 39-55. doi : 10.5802/afst.1622. https://afst.centre-mersenne.org/articles/10.5802/afst.1622/

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