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A characterization of the Hilbert transform

Author(s): Nicola Arcozzi; Luigi Fontana
Journal: Proc. Amer. Math. Soc. 126 (1998), 1747-1749.
MSC (1991): Primary 42A50
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Abstract: In this note the Hilbert transform is characterized in terms of function algebras with respect to pointwise multiplication.

References:

[Co]: M. Cótlar, A combinatorial inequality and its applications to spaces, Revista Mat. Cuyana, 1, 2, 1955, pp. 105-168. MR 18:219a
[Du]: P. L. Duren, Theory of spaces, Academic Press, New York, London, 1970. MR 42:3552
[GK]: T.S. Gokhberg, N. Ya. Krupnik, Norm of the Hilbert tranformation in the space, Func. An. and its Appl, 1968, pp. 180-1.
[Pi]: S. K. Pichorides, On the best value of the constants in the theorems of M. Riesz, Zygmund and Kolmogorov, Studia Math., 44, 1972, pp. 165-179. MR 47:702
[SW]: E. M. Stein, G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton U.P., Princeton N.J., 1971. MR 46:4102


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