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Journal of Fourier Analysis and Applications

, Volume 25, Issue 6, pp 3310–3341 | Cite as

The Boas Problem on Hankel Transforms

  • A. DebernardiEmail author
Article
  • 66 Downloads

Abstract

Norm equivalences between a function and its Hankel transform are studied both in the context of weighted Lebesgue spaces with power weights, and in Lorentz spaces. Boas-type results involving real-valued general monotone functions are obtained. Corresponding results for the Fourier transform are also given.

Keywords

Boas conjecture Hankel transform General monotonicity Weighted Lebesgue spaces Lorentz spaces 

Mathematics Subject Classification

Primary 42A38 26D15 Secondary 26A48 

Notes

Acknowledgements

The author acknowledges the remarks of the anonymous referee that contributed to significantly improve the manuscript. This research was partially funded by the CERCA Programme of the Generalitat de Catalunya, Centre de Recerca Matemàtica, the Grant MTM2017–87409–P from the Spanish Ministerio de Economía, Industria y Competitividad, the ERC starting grant No. 713927, and the ISF Grant No. 447/16.

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Authors and Affiliations

  1. 1.Department of MathematicsBar-Ilan UniversityRamat-GanIsrael
  2. 2.Centre de Recerca MatemàticaBarcelonaSpain

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