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Fourier Inequalities With Ap-Weights

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General Inequalities 5

Abstract

In this paper weighted Fourier inequalities are established with weights in the Ap-class of Muckenhoupt. Specifically, for even, non-decreasing weights on (0, ∞) the weight conditions are necessary and sufficient for the Paley-Titchmarsh inequality and its extensions. For decreasing weights the inequalities fail.

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References

  1. J.J. Benedetto and H.P. Heinig, Weighted Hardy spaces and the Laplace transform. Harmonic Anal. Conf., Cortona, Italy, 1982. Lect. Notes in Math. 992, Springer Verlag,xxx 240–277.

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Authors and Affiliations

  1. Department of Mathematics, University of Maryland, 20742, College Park, Maryland, USA

    J. J. Benedetto & R. Johnson

  2. Department of Mathematics, McMaster University, L8S 4K1, Hamilton, Ontario, Canada

    H. P. Heinig

Authors
  1. J. J. Benedetto
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  2. H. P. Heinig
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  3. R. Johnson
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Editor information

Editors and Affiliations

  1. Mathematisches Institut I, Universität Karlsruhe, Kaiserstraße 12, D-7500, Karlsruhe 1, Germany

    Wolfgang Walter

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© 1987 Birkhäuser Verlag Basel

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Benedetto, J.J., Heinig, H.P., Johnson, R. (1987). Fourier Inequalities With Ap-Weights. In: Walter, W. (eds) General Inequalities 5. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik Série internationale d’Analyse numérique, vol 80. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7192-1_17

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  • DOI: https://doi.org/10.1007/978-3-0348-7192-1_17

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-7194-5

  • Online ISBN: 978-3-0348-7192-1

  • eBook Packages: Springer Book Archive

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