On the p-norm of an Integral Operator in the Half Plane
Canadian mathematical bulletin, Tome 56 (2013) no. 3, pp. 593-601

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2011-186-3
Mots-clés : 47B38, 47G10, 32A36, Bergman projection, integral operator, Lp-norm, the upper half plane
Liu, Congwen; Zhou, Lifang. On the p-norm of an Integral Operator in the Half Plane. Canadian mathematical bulletin, Tome 56 (2013) no. 3, pp. 593-601. doi: 10.4153/CMB-2011-186-3
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[1] [1] Bañuelos, R. and Janakiraman, P., Lp-bounds for the Beurling-Ahlfors transform. Trans. Amer. Math. Soc. 360 (2008), no. 7, 3603–3612. Google Scholar | DOI

[2] [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] [3] Dostanić, M., Norm of the Berezin transform on Lp spaces. J. Anal. Math. 104 (2008), 13–23. Google Scholar | DOI

[4] [4] Erdélyi, A., Magnus, W., Oberhettinger, F., and Tricomi, F. G., Higher transcendental functions. VoI, l., McGraw-Hill, New York, 1953. Google Scholar

[5] [5] Hardy, G. H., Littlewood, J. E., and G. Pólya, Inequalities. Second ed., Cambridge University Press, Cambridge, 1952. Google Scholar

[6] [6] Iwaniec, T., Extremal inequalities in Sobolev spaces and quasiconformal mappings. Z. Anal. Anwendungen 1 (1982), no. 6, 1–16. Google Scholar

[7] [7] Iwaniec, T. and Martin, G., Riesz transforms and related singular integrals. J. Reine Angew. Math. 473 (1996), 25–57. Google Scholar

[8] [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] [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

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