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A note on the boundedness of Bergman-type operators on mixed norm spaces

Part of: Linear function spaces and their duals Special classes of linear operators Holomorphic functions of several complex variables

Published online by Cambridge University Press:  09 April 2009

Zengjian Lou
Zengjian Lou
Affiliation:
Department of MathematicsShantou UniversityShantou Guangdong 515063P. R. Chinazjlou@stu.edu.cn
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Abstract

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We prove the boundedness of Bergman-type operators on mixed norm spaces Lp·q (φ) for 0 < q < 1 and 0 < p ≤ ∞ of functions on the unit ball of ” with an application to Gleason's problem.

Keywords

Bergman-type operatorsmixed norm spacesboundedness.

MSC classification

Secondary: 47B38: Operators on function spaces (general) 32A30: Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30) 46E15: Banach spaces of continuous, differentiable or analytic functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 82 , Issue 3 , June 2007 , pp. 395 - 402
Copyright
Copyright © Australian Mathematical Society 2007

References

[1]Beatrous, F. and Burbea, J., ‘Holomorphic sobolev spaces on the ball’, Dissertationes Math. (Rozprawy Mat.) 276 (1989), 60 pages.Google Scholar
[2]Hardy, G. H. and Littlewood, J. E., ‘Some properties of fractional integrals II’, Math. Z. 34 (1932). 403–439.CrossRefGoogle Scholar
[3]Liu, Y., ‘Boundedness of the Bergman type operators on mixed norm spaces’, Proc. Amer. Math. Soc. 130 (2002), 2363–2367.CrossRefGoogle Scholar
[4]Ren, G. and Shi, J., ‘Bergman type operator on mixed norm spaces with applications’, Chinese Ann. Math. Ser. B 18 (1997), 265–276.Google Scholar
[5]Rudin, W., Function theory in the unit ball of ” (Springer, New York, 1980).CrossRefGoogle Scholar
[6]Shields, A. L. and Williams, D. L., ‘Bounded projection, duality and multipliers in spaces of analytic functions’, Trans. Amer. Math. Soc. 162 (1971), 287–302.Google Scholar