Combinatorial property of all positive measures in dimensions $2$ and $3$

Pavel Mozolyako; Georgios Psaromiligkos; Alexander Volberg; Pavel Zorin Kranich

doi:10.5802/crmath.90

Analyse, Analyse harmonique

Combinatorial property of all positive measures in dimensions

2

and

3

Pavel Mozolyako ^1,² ; Georgios Psaromiligkos ² ; Alexander Volberg ² ; Pavel Zorin Kranich ³

¹ Department of Mathematics and Computer Science, Saint Petersburg State University, Saint Petersburg, 199178, Russia
² Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
³ Department of Mathematics, University of Bonn, Bonn, 51011, Germany

Comptes Rendus. Mathématique, Volume 358 (2020) no. 6, pp. 721-725.

Résumé

We prove multi-parameter dyadic embedding theorem for Hardy operator on the multi-tree. We also show that for a large class of Dirichlet spaces of holomorphic functions in bi-disc and tri-disc this proves the embedding theorem of those spaces on bi- and tri-disc. We completely describe the Carleson measures for such embeddings.

Reçu le : 2020-02-10
Révisé le : 2020-06-25
Accepté le : 2020-06-26
Publié le : 2020-10-02

DOI : 10.5802/crmath.90

Affiliations des auteurs :

Pavel Mozolyako ^{1, 2} ; Georgios Psaromiligkos ² ; Alexander Volberg ² ; Pavel Zorin Kranich ³

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

@article{CRMATH_2020__358_6_721_0,
     author = {Pavel Mozolyako and Georgios Psaromiligkos and Alexander Volberg and Pavel Zorin Kranich},
     title = {Combinatorial property of all positive measures in dimensions $2$ and $3$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {721--725},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {6},
     year = {2020},
     doi = {10.5802/crmath.90},
     language = {en},
}

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Pavel Mozolyako; Georgios Psaromiligkos; Alexander Volberg; Pavel Zorin Kranich. Combinatorial property of all positive measures in dimensions $2$ and $3$. Comptes Rendus. Mathématique, Volume 358 (2020) no. 6, pp. 721-725. doi : 10.5802/crmath.90. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.90/

Bibliographie
Cité par

[1] Nicola Arcozzi; Irina Holmes; Pavel Mozolyako; Alexander Volberg Bi-parameter embedding and measures with restriction energy condition (2018) (https://arxiv.org/abs/1811.00978) | Zbl

[2] Nicola Arcozzi; Pavel Mozolyako; Karl-Mikael Perfekt; Giulia Sarfatti Carleson measures for the Dirichlet space on the bidisc (2018) (https://arxiv.org/abs/1811.04990)

[3] Nicola Arcozzi; Pavel Mozolyako; Georgios Psaromiligkos; Alexander Volberg; Pavel Zorin-Kranich Bi-parameter Carleson embeddings with product weights (2019) (https://arxiv.org/abs/1906.11150)

[4] Nicola Arcozzi; Pavel Mozolyako; Georgios Psaromiligkos; Alexander Volberg; Pavel Zorin-Kranich Carleson embedding on tri-tree and on tri-disc (2020) (https://arxiv.org/abs/2001.02373)

[5] Nicola Arcozzi; Richard Rochberg; Eric T. Sawyer; Brett D. Wick Potential theory on trees, graphs and Ahlfors-regular metric spaces, Potential Anal., Volume 41 (2014) no. 2, pp. 317-366 | DOI | MR | Zbl

[6] Fedor Nazarov; Sergei Treil; Alexander Volberg The Bellman functions and two-weight inequalities for Haar multipliers, J. Am. Math. Soc., Volume 12 (1999) no. 4, pp. 909-928 | DOI | MR | Zbl

[7] Eric T. Sawyer Weighted inequalities for the two-dimensional Hardy operator, Stud. Math., Volume 82 (1985) no. 1, pp. 1-16 | DOI | MR | Zbl

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