Czechoslovak Mathematical Journal, first online, pp. 1-21


Inclusion relations between harmonic Bergman-Besov and weighted Bloch spaces on the unit ball

Ömer Faruk Doğan, Adem Ersin Üreyen

Received September 8, 2017.   Published online August 8, 2018.

Abstract:  We consider harmonic Bergman-Besov spaces $b^p_\alpha$ and weighted Bloch spaces $b^\infty_\alpha$ on the unit ball of $\mathbb{R}^n$ for the full ranges of parameters $0<p<\infty$, $\alpha\in\mathbb{R}$, and determine the precise inclusion relations among them. To verify these relations we use Carleson measures and suitable radial differential operators. For harmonic Bergman spaces various characterizations of Carleson measures are known. For weighted Bloch spaces we provide a characterization when $\alpha>0$.
Keywords:  harmonic Bergman-Besov space; weighted harmonic Bloch space; Carleson measure; Berezin transform
Classification MSC:  31B05, 42B35
DOI:  10.21136/CMJ.2018.0422-17

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Affiliations:  Ömer Faruk Doğan, Department of Mathematics, Tekirdağ Namik Kemal University, Kampüs Cad No:1, 59030 Süleymanpaşa/Tekirdağ, Turkey, e-mail: ofdogan@nku.edu.tr; Adem Ersin Üreyen, Department of Mathematics, Anadolu University, Yeşiltepe Mahallesi, Yunus Emre Kampüsü, 26470 Tepebaşi/Eskişehir, Turkey, e-mail: aeureyen@anadolu.edu.tr


 
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