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On the p-norm of an Integral Operator in the Half Plane

Published online by Cambridge University Press:  20 November 2018

Congwen Liu  and
Lifang Zhou
Congwen Liu
Affiliation:
School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China e-mail: [email protected] Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences e-mail: e-mail: [email protected]
Lifang Zhou
Affiliation:
Department ofMathematics, Huzhou Teachers College, Huzhou, Zhejiang 313000, People’s Republic of China
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Abstract.

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We give a partial answer to a conjecture of Dostanić on the determination of the norm of a class of integral operators induced by the weighted Bergman projection in the upper half plane.

Keywords

47B3847G1032A36Bergman projectionintegral operatorLp-normthe upper half plane
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 3 , 01 September 2013 , pp. 593 - 601
Copyright
Copyright © Canadian Mathematical Society 2013

References

[1] Bañuelos, R. and Janakiraman, P., Lp-bounds for the Beurling-Ahlfors transform. Trans. Amer. Math. Soc. 360 (2008), no. 7, 3603–3612. http://dx.doi.org/10.1090/S0002-9947-08-04537-6 Google Scholar
[2] Dostanić, M., Integral operators induced by Bergman type kernels in the half plane. Asymptot. Anal. 67 (2010), no. 3–4, 217–228.Google Scholar
[3] Dostanić, M., Norm of the Berezin transform on Lp spaces. J. Anal. Math. 104 (2008), 13–23. http://dx.doi.org/10.1007/s11854-008-0014-8 Google Scholar
[4] Erdélyi, A., Magnus, W., Oberhettinger, F., and Tricomi, F. G., Higher transcendental functions. VoI, l., McGraw-Hill, New York, 1953.Google Scholar
[5] Hardy, G. H., Littlewood, J. E., and G. Pólya, Inequalities. Second ed., Cambridge University Press, Cambridge, 1952.Google Scholar
[6] Iwaniec, T., Extremal inequalities in Sobolev spaces and quasiconformal mappings. Z. Anal. Anwendungen 1 (1982), no. 6, 1–16.Google Scholar
[7] Iwaniec, T. and Martin, G., Riesz transforms and related singular integrals. J. Reine Angew. Math. 473 (1996), 25–57.Google Scholar
[8] Pichorides, S. K., On the best values of the constants in the theorems of Riesz M., Zygmund and Kolmogorov. Studia Math. 44 (1972), 165–179.Google Scholar
[9] Zhu, K., A sharp norm estimate of the Bergman projection in Lp spaces. In: Bergman spaces and related topices in complex analysis, Contemp. Math., 404, American Mathematical Society, Providence, RI, 2006, pp. 199–205.Google Scholar