Some inequalities related to the Hausdorff-Young theorem
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- by W. T. Sledd PDF
- Proc. Amer. Math. Soc. 42 (1974), 535-540 Request permission
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
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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.
G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Cambridge Univ. Press, New York, 1934.
- James H. Hedlund, Multipliers of $H^{p}$ spaces, J. Math. Mech. 18 (1968/1969), 1067–1074. MR 0243080
- C. N. Kellogg, An extension of the Hausdorff-Young theorem, Michigan Math. J. 18 (1971), 121–127. MR 280995 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.
- A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 42 (1974), 535-540
- MSC: Primary 42A18
- DOI: https://doi.org/10.1090/S0002-9939-1974-0344780-7
- MathSciNet review: 0344780