Geodesic
Extended Cesàro operators between Hardy and Bergman spaces on the complex ball
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 67-72 
E. S. Dubtsov. Extended Cesàro operators between Hardy and Bergman spaces on the complex ball. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 67-72. http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a6/
@article{ZNSL_2018_467_a6,
     author = {E. S. Dubtsov},
     title = {Extended {Ces\`aro} operators between {Hardy} and {Bergman} spaces on the complex ball},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {67--72},
     year = {2018},
     volume = {467},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a6/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We characterize those holomorphic symbols $g$ for which the extended Cesàro operator $V_g$ maps the Hardy space $H^p(B)$ into the weighted Bergman space $A^q_\beta(B)$, $0, $\beta>-1$, on the unit ball $B$ of $\mathbb C^d$.

[1] A. Aleman, J. A. Cima, “An integral operator on $H^p$ and Hardy's inequality”, J. Anal. Math., 85 (2001), 157–176 | DOI | MR | Zbl

[2] A. Aleman, A. G. Siskakis, “An integral operator on $H^p$”, Complex Variables Theory Appl., 28:2 (1995), 149–158 | DOI | MR | Zbl

[3] A. Aleman, A. G. Siskakis, “Integration operators on Bergman spaces”, Indiana Univ. Math. J., 46:2 (1997), 337–356 | DOI | MR | Zbl

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

[5] D. H. Luecking, “Embedding derivatives of Hardy spaces into Lebesgue spaces”, Proc. London Math. Soc. (3), 63:3 (1991), 595–619 | DOI | MR | Zbl

[6] J. Pau, “Integration operators between Hardy spaces on the unit ball of $\mathbb C^n$”, J. Funct. Anal., 270:1 (2016), 134–176 | DOI | MR | Zbl

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

[8] Z. Wu, “Volterra operator, area integral and Carleson measures”, Sci. China Math., 54:11 (2011), 2487–2500 | DOI | MR | Zbl

[9] J. Xiao, “Riemann–Stieltjes operators between weighted Bergman spaces”, Complex and harmonic analysis, DEStech Publ., Inc., Lancaster, PA, 2007, 205–212 | MR | Zbl

[10] K. Zhu, Spaces of holomorphic functions in the unit ball, Graduate Texts in Mathematics, 226, Springer-Verlag, New York, 2005 | MR | Zbl