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Some inequalities related to the Hausdorff-Young theorem

Author: W. T. Sledd
Journal: Proc. Amer. Math. Soc. 42 (1974), 535-540
MSC: Primary 42A18
MathSciNet review: 0344780
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Abstract: The classical Hausdorff-Young inequalities for Fourier series are extended. These new results are then used to improve known results on multipliers of $ {H^p}$ spaces.

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

  • [1] G. H. Hardy and J. E. Littlewood, Notes on the theory of series. XX: Generalizations of a theorem of Paley, Quart. J. Math. Oxford Ser. 8 (1937), 161-171.
  • [2] G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Cambridge Univ. Press, New York, 1934.
  • [3] James H. Hedlund, Multipliers of 𝐻^{𝑝} spaces, J. Math. Mech. 18 (1968/1969), 1067–1074. MR 0243080
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  • [5] J. E. Littlewood and R. E. A. C. Paley, Theorems on Fourier series and power series. II, Proc. London Math. Soc. 42 (1936), 52-89.
  • [6] A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776

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Keywords: Multipliers of $ {H^p}$ spaces, Littlewood-Paley theorems, Hausdorff-Young inequalities
Article copyright: © Copyright 1974 American Mathematical Society