Abstract
In this paper we describe the image of the Hilbert transform operator for Bergman space.
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REFERENCES
B. A. Derzhavets, “Spaces of functions analytic on the convex domains Cn and having a given behavior near the boundary” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 276 (1984), no. 6, 1297–1300.
Yu. I. Lyubarskii, “The Wiener-Paley theorem for convex sets,” Izv. Akad. Armyan. SSR Ser. Mat. [Soviet J. Contemporary Math. Anal.], 62 (1988), no. 2, 162–172.
V. I. Lutsenko and R. S. Yulmukhametov, “A generalization of the Wiener-Paley theorem to functionals in Smirnov spaces,” Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.], 200 (1991), 245–254.
V. V. Napalkov, Jr. and R. S. Yulmukhametov, “On the Cauchy transforms for functionals on Bergman space,” Mat. Sb. [Russian Acad. Sci. Sb. Math.], 185 (1994), no. 7, 77–86.
G. Köthe, “Dualität in der Funktionentheorie,” J. Reine Angew. Math., 191 (1953), no. 1/2, 30–49.
L. Hörmander, The Analysis of Linear Partial Differential Operators, vol. 2, Springer-Verlag, Heidelberg, 1983.
R. S. Yulmukhametov, “The space of analytic functions of given growth near the boundary” Mat. Zametki [Math. Notes], 32 (1982), no. 1, 41–57.
V. V. Napalkov, “Spaces of analytic functions of given growth near the boundary,” Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.], 51 (1987), no. 2, 287–305.
O. V. Epifanov, “Duality of a pair of spaces of analytic functions of bounded growth,” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 319 (1991), no. 6, 1297–1300.
S. A. Merenkov, “On the Cauchy image of Bergman space,” in: Mathematical Physics, Calculus, Geometry, Kharkov, 1999.
A. P. Calderon, “Cauchy integrals on Lipschitz curves and related operators,” Proc. Mat. Acad. Sci. USA (1977), 1324–1327.
R. R. Coifman, A. McIntosh, and Y. Meyer, “L'intégrale de Cauchy définit un opérateur borné sur L 2 pour les courbes Lipschitziennes,” Annals of Math., 116 (1982), no. 2.
E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Math. Ser., Princeton Univ. Press, Princeton, N.J., 1970.
G. M. Goluzin, A Geometric Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow, 1966.
S. L. Krushkal and R. Künau, Quasiconformal mappings. New Methods and Applications [in Russian],Nauka, Novosibirsk,1984.
D. Gaier, Vorlesungen über Approximation im Komplexen, Birkhäuser, Basel, 1984.
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Napalkov, V.V., Yulmukhametov, R.S. On the Hilbert Transform in Bergman Space. Mathematical Notes 70, 61–70 (2001). https://doi.org/10.1023/A:1010221901553
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DOI: https://doi.org/10.1023/A:1010221901553