Hankel Transforms of General Monotone Functions

  • Alberto Debernardi
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


We show that the Hankel transform of a general monotone function converges uniformly if and only if the limit function is bounded. To this end, we rely on an Abel–Olivier test for real-valued functions. Analogous results for cosine series are derived as well. We also show that our statements do not hold without the general monotonicity assumption in the case of cosine integrals and series.


Hankel transform Boundedness Uniform convergence General monotonicity Cosine series 

AMS 2010 Subject Classification

Primary: 42A38; Secondary: 42A20 44A20 



This research was partially funded by the ERC starting grant No. 713927, the ISF grant No. 447/16, the CERCA Programme of the Generalitat de Catalunya, Centre de Recerca Matemàtica, and the MTM-2014-59174-P grant.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Alberto Debernardi
    • 1
    • 2
  1. 1.Bar-Ilan UniversityRamat-GanIsrael
  2. 2.Centre de Recerca MatemàticaBellaterraSpain

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