Sparse Brudnyi and John–Nirenberg Spaces

Domínguez, Óscar; Milman, Mario

doi:10.5802/crmath.252

Analyse fonctionnelle

Sparse Brudnyi and John–Nirenberg Spaces

Domínguez, Óscar ¹ ; Milman, Mario ²

¹ O. Domínguez, Departamento de Análisis Matemático y Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid, Spain.
² M. Milman, Instituto Argentino de Matematica, Buenos Aires, Argentina

Comptes Rendus. Mathématique, Tome 359 (2021) no. 8, pp. 1059-1069.

Résumé

A generalization of the theory of Y. Brudnyi [7], and A. and Y. Brudnyi [5, 6], is presented. Our construction connects Brudnyi’s theory, which relies on local polynomial approximation, with new results on sparse domination. In particular, we find an analogue of the maximal theorem for the fractional maximal function, solving a problem proposed by Kruglyak–Kuznetsov. Our spaces shed light on the structure of the John–Nirenberg spaces. We show that $S J N_{p}$ (sparse John–Nirenberg space) coincides with $L^{p}, 1 < p < \infty .$ This characterization yields the John–Nirenberg inequality by extrapolation and is useful in the theory of commutators.

Reçu le : 2021-07-11
Accepté le : 2021-08-01
Publié le : 2021-10-08

DOI : 10.5802/crmath.252

Classification : 42B35, 42B25, 46E30, 46E35

Affiliations des auteurs :

Domínguez, Óscar ¹ ; Milman, Mario ²

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     title = {Sparse {Brudnyi} and {John{\textendash}Nirenberg} {Spaces}},
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Domínguez, Óscar; Milman, Mario. Sparse Brudnyi and John–Nirenberg Spaces. Comptes Rendus. Mathématique, Tome 359 (2021) no. 8, pp. 1059-1069. doi : 10.5802/crmath.252. http://www.numdam.org/articles/10.5802/crmath.252/

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