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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A characterization of the Hilbert transform


Authors: Nicola Arcozzi and Luigi Fontana
Journal: Proc. Amer. Math. Soc. 126 (1998), 1747-1749
MSC (1991): Primary 42A50
MathSciNet review: 1443810
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Abstract | References | Similar Articles | Additional Information

Abstract: In this note the Hilbert transform is characterized in terms of function algebras with respect to pointwise multiplication.


References [Enhancements On Off] (What's this?)

  • [Co] M. Cotlar, A combinatorial inequality and its applications to 𝐿²-spaces, Rev. Mat. Cuyana 1 (1955), 41–55 (1956). MR 0080263 (18,219a)
  • [Du] Peter L. Duren, Theory of 𝐻^{𝑝} spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655 (42 #3552)
  • [GK] T.S. Gokhberg, N. Ya. Krupnik, Norm of the Hilbert tranformation in the $L^p$ space, Func. An. and its Appl, 1968, pp. 180-1.
  • [Pi] S. K. Pichorides, On the best values of the constants in the theorems of M. Riesz, Zygmund and Kolmogorov, Studia Math. 44 (1972), 165–179. (errata insert). Collection of articles honoring the completion by Antoni Zygmund of 50 years of scientific activity, II. MR 0312140 (47 #702)
  • [SW] Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton University Press, Princeton, N.J., 1971. Princeton Mathematical Series, No. 32. MR 0304972 (46 #4102)

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Additional Information

Nicola Arcozzi
Affiliation: Università di Milano, Dipartimento di Matematica, “Federico Enriques", Via C. Saldini, 50, 20133 Milano, Italy
Email: arcozzi@mat.unimi.it

Luigi Fontana
Affiliation: Università di Milano, Dipartimento di Matematica, “Federico Enriques", Via C. Saldini, 50, 20133 Milano, Italy
Email: fontana@mat.unimi.it

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04214-2
PII: S 0002-9939(98)04214-2
Received by editor(s): August 20, 1996
Received by editor(s) in revised form: December 1, 1996
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1998 American Mathematical Society