Geodesic
Carleson measures for weighted harmonic mixed norm spaces on bounded domains in $\mathbb {R}^n$
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 4, pp. 1205-1216
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We study weighted mixed norm spaces of harmonic functions defined on smoothly bounded domains in $\mathbb {R}^n$. Our principal result is a characterization of Carleson measures for these spaces. First, we obtain an equivalence of norms on these spaces. Then we give a necessary and sufficient condition for the embedding of the weighted harmonic mixed norm space into the corresponding mixed norm space.
We study weighted mixed norm spaces of harmonic functions defined on smoothly bounded domains in $\mathbb {R}^n$. Our principal result is a characterization of Carleson measures for these spaces. First, we obtain an equivalence of norms on these spaces. Then we give a necessary and sufficient condition for the embedding of the weighted harmonic mixed norm space into the corresponding mixed norm space.
DOI : 10.21136/CMJ.2022.0018-22
Classification : 31B05, 42B35
Keywords: harmonic function; mixed norm space; Carleson measure 
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Savković, Ivana. Carleson measures for weighted harmonic mixed norm spaces on bounded domains in $\mathbb {R}^n$. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 4, pp. 1205-1216. doi: 10.21136/CMJ.2022.0018-22

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