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Israel Journal of Mathematics

, Volume 6, Issue 2, pp 133–149 | Cite as

Extensions of the Hausdorff-Young theorem

  • M. M. Rao
Article

Abstract

In this paper the clasical Hausdorff-Young theorem, which states that iffL p, 1≦p≦2, on the line and\(\hat f\) is its Fourier transform, then\(\left\| {\hat f} \right\|_q \leqq \left\| f \right\|_p \) whereq −1+p −1=1, is extended in two ways for certain Orlicz spacesL Φ. IfL Φ is based on (G, μ), (1) an arbitrary compact topological group with Haar measure, and (2) a locally compact abelian topological group andμ is again the Haar measure, then the above inequality is extended to these cases. Various other related results and remarks are also included.

Keywords

Compact Group Haar Measure Orlicz Space Compact Abelian Group Sublinear Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University 1968

Authors and Affiliations

  • M. M. Rao
    • 1
  1. 1.Carnegie-Mellon UniversityPittsburgh

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