Geodesic
Operators on the Besov spaces of holomorphic functions on the unit ball in $\mathbb{C}^n$
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 2, pp. 139-145 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the present paper we consider the Toeplitz-$T^{\alpha}_{\bar{h}}$ and differentiation-$D^{\delta}$ operators on the Besov spaces $B_p(\beta)$ for all $0$. We show that $T^{\alpha}_{\bar{h}}:B_p(\beta)\rightarrow B_p(\beta)$ for $\bar{h}\in H^{\infty}(B^n)$ and $D^{\delta}:B_p(\beta)\rightarrow B_p(\tilde\beta)$ where $\widetilde\beta=\beta+p\delta$.
Keywords: weighted Besov spaces, unit ball, projection. 
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A. V. Harutyunyan; W. Lusky. Operators on the Besov spaces of holomorphic functions on the unit ball in $\mathbb{C}^n$. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 2, pp. 139-145. http://geodesic.mathdoc.fr/item/UZERU_2017_51_2_a0/

[1] A. Harutyunyan, W. Lusky, “$\omega$-Weighted Holomorphic Besov Spaces”, Comment. Math. Univ. Carolin., 52:1 (2011,), 37–56 | MR | Zbl

[2] J. Arazy, S. Fisher, J. Peetre, “Möbius Invariant Function Spaces”, J. Reine Angew. Math., 363 (1985), 110–145 | MR | Zbl

[3] K. Stroethoff, “Besov Type Characterisations for the Bloch Space”, Bull. Australian Math. Soc., 39 (1989), 405–420 | DOI | MR | Zbl

[4] A. Harutyunyan, W. Lusky, “Holomorphic Bloch Spaces on the Unit Ball in $\mathbb{C}^n$”, Comment. Math. Univ. Carolin., 50:4 (2009), 549–562 | MR | Zbl

[5] M. Nowak, “Bloch and Möbius Invariant Besov Spaces on the Unit Ball of $\mathbb{C}^n$”, Complex Var., 44 (2001), 1–12 | DOI | MR | Zbl

[6] S. Li, S. Stević, “Some Characterizations of the Besov Space and the $\alpha$-Bloch Space.”, J. Math. Anal. Appl., 346 (2008), 262–273 | DOI | MR | Zbl

[7] S. Li, H. Wulan, “Besov Space in the Unit Ball”, Indian J. Math., 48:2 (2006), 177–186 | MR | Zbl

[8] A. Djrbashian, F. Shamoyan, Topics in the Theory of $A^p(\alpha)$ Spaces, Teubner Texte Math., Leipzig, 1988 | MR

[9] K. Zhu, Spaces of Holomorphic Functions in the Unit Ball, Springer, 2004 | MR