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.
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Pavel Mozolyako 1, 2; Georgios Psaromiligkos 2; Alexander Volberg 2; Pavel Zorin Kranich 3
@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}, }
TY - JOUR AU - Pavel Mozolyako AU - Georgios Psaromiligkos AU - Alexander Volberg AU - Pavel Zorin Kranich TI - Combinatorial property of all positive measures in dimensions $2$ and $3$ JO - Comptes Rendus. Mathématique PY - 2020 SP - 721 EP - 725 VL - 358 IS - 6 PB - Académie des sciences, Paris DO - 10.5802/crmath.90 LA - en ID - CRMATH_2020__358_6_721_0 ER -
%0 Journal Article %A Pavel Mozolyako %A Georgios Psaromiligkos %A Alexander Volberg %A Pavel Zorin Kranich %T Combinatorial property of all positive measures in dimensions $2$ and $3$ %J Comptes Rendus. Mathématique %D 2020 %P 721-725 %V 358 %N 6 %I Académie des sciences, Paris %R 10.5802/crmath.90 %G en %F CRMATH_2020__358_6_721_0
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/
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