Classical operators on Bloch spaces
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 37, Tome 366 (2009), pp. 42-52 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $\mathbb D^n$ denote the unit polydisc and let $B_n$ denote the unit ball in $\mathbb C^n$, $n\ge1$. We investigate weighted composition operators on the $\alpha$-Bloch spaces $\mathcal B^\alpha(\mathbb D^n)$, $\alpha>1$. Also, we study Cesàro type operators on the $\alpha$-Bloch spaces $\mathcal B^\alpha(B_n)$, $\alpha>0$. Bibl. – 15 titles.
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E. S. Dubtsov. Classical operators on Bloch spaces. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 37, Tome 366 (2009), pp. 42-52. http://geodesic.mathdoc.fr/item/ZNSL_2009_366_a2/

[1] L. Carleson, “An interpolation problem for bounded analytic functions”, Amer. J. Math., 80 (1958), 921–930 | DOI | MR | Zbl

[2] C. C. Cowen, B. D. MacCluer, Composition operators on spaces of analytic functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1995 | MR | Zbl

[3] E. Doubtsov, “Growth spaces on circular domains: composition operators and Carleson measures”, C. R. Math. Acad. Sci. Paris, 347:11–12 (2009), 609–612 | DOI | MR | Zbl

[4] E. S. Dubtsov, “Vesovye operatory kompozitsii na prostranstvakh rosta”, Sib. matem. zhurn. (to appear)

[5] P. M. Gauthier, J. Xiao, “BiBloch-type maps: existence and beyond”, Complex Var. Theory Appl., 47:8 (2002), 667–678 | DOI | MR | Zbl

[6] Z. Hu, “Extended Cesàro operators on mixed norm spaces”, Proc. Amer. Math. Soc., 131:7 (2003), 2171–2179 | DOI | MR | Zbl

[7] H. T. Kaptanoğlu, “Carleson measures for Besov spaces on the ball with applications”, J. Funct. Anal., 250:2 (2007), 483–520 | DOI | MR | Zbl

[8] S. Li, S. Stević, “Riemann–Stieltjes-type integral operators on the unit ball in $\mathbb C_n$”, Complex Var. Elliptic Equ., 52:6 (2007), 495–517 | DOI | MR | Zbl

[9] S. Li, S. Stević, “Weighted composition operators from $\alpha$-Bloch space to $H_\infty$ on the polydisc”, Numer. Funct. Anal. Optim., 28:7–8 (2007), 911–925 | MR | Zbl

[10] Ch. Pommerenke, “Schlichte Funktionen und analytische Funktionen von beschränkter mittlerer Oszillation”, Comment. Math. Helv., 52:4 (1977), 591–602 | DOI | MR | Zbl

[11] U. Rudin, Teoriya funktsii v edinichnom share iz $\mathbb C^n$, Mir, M., 1984 | MR | Zbl

[12] M. Tjani, “Compact composition operators on Besov spaces”, Trans. Amer. Math. Soc., 355:11 (2003), 4683–4698 | DOI | MR | Zbl

[13] J. Xiao, “Riemann–Stieltjes operators on weighted Bloch and Bergman spaces of the unit ball”, J. London Math. Soc. (2), 70:1 (2004), 199–214 | DOI | MR | Zbl

[14] R. Yoneda, “Pointwise multipliers from BMOA$^\alpha$ to BMOA$^\beta$”, Complex Var. Theory Appl., 49:14 (2004), 1045–1061 | DOI | MR | Zbl

[15] R. Yoneda, “Multiplication operators, integration operators and companion operators on weighted Bloch space”, Hokkaido Math. J., 34:1 (2005), 135–147 | DOI | MR | Zbl