# zbMATH — the first resource for mathematics

A class of integral operators on mixed norm spaces in the unit ball. (English) Zbl 1174.47349
Summary: This article provides some sufficient or necessary conditions for a class of integral operators to be bounded on mixed norm spaces in the unit ball.

##### MSC:
 47G10 Integral operators 30H05 Spaces of bounded analytic functions of one complex variable
##### Keywords:
integral operator; mixed norm space; boundedness
Full Text:
##### References:
 [1] A. Benedek and R. Panzone: The spaces L p with mixed norm. Duke Math. J. 28 (1961), 301–324. · Zbl 0107.08902 [2] B. R. Choe: Projections, the weighted Bergman spaces, and the Bloch space. Proc. Am. Math. Soc. 108 (1990), 127–136. · Zbl 0684.47022 [3] F. Forelli and W. Rudin: Projections on spaces of holomorphic functions in balls. Indiana Univ. Math. J. 24 (1974), 593–602. · Zbl 0297.47041 [4] S. Gadbois: Mixed-norm generalizations of Bergman space and duality. Proc. Am. Math. Soc. 104 (1988), 1171–1180. · Zbl 0691.32002 [5] C. Kolaski: A new look at a theorem of Forelli and Rudin. Indiana Univ. Math. J. 28 (1979), 495–499. · Zbl 0412.41023 [6] O. Kurens and K. H. Zhu: A class of integral operators on the unit ball of $$\mathbb{C}$$n. Integr. Equ. Oper. Theory 56 (2006), 71–82. · Zbl 1109.47041 [7] Y. M. Liu: Boundedness of the Bergman type operators on mixed norm space. Proc. Am. Math. Soc. 130 (2002), 2363–2367. · Zbl 1020.47024 [8] G. B. Ren and J. H. Shi: Bergman type operator on mixed norm spaces with applications. Chin. Ann. Math., Ser. B 18 (1997), 265–276. · Zbl 0891.47019 [9] G. B. Ren and J. H. Shi: Forelli-Rudin type theorem on pluriharmonic Bergman spaces with small exponent. Sci. China, Ser. A 42 (1999), 1286–1291. · Zbl 0955.46016 [10] G. B. Ren and J. H. Shi: Gleason’s problem in weighted Bergman space on egg domains. Sci. China, Ser. A 41 (1998), 225–231. · Zbl 0912.32018 [11] A. L. Shields and D. L. Williams: Bounded projections, duality and multipliers in spaces of analytic functions. Trans. Am. Math. Soc. 162 (1971), 287–302. · Zbl 0227.46034 [12] K. H. Zhu: The Bergman spaces, the Bloch spaces and Gleason’s problem. Trans. Am. Math. Soc. 309 (1988), 253–268. · Zbl 0657.32002 [13] K. H. Zhu: Spaces of Holomorphic Functions in the Unit Ball. Graduate Texts in Mathematics 226. Springer-Verlag, New York, 2005.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.