Acta Mathematica Hungarica

, Volume 159, Issue 2, pp 374–399 | Cite as

Functions of bounded p-variation and weighted integrability of Fourier transforms

  • S. A. Krayukhin
  • S. S. VolosivetsEmail author


We study some properties of functions of bounded p-variation on \(\mathbb{R}\) and its specific fractional moduli of smoothness, including the connection between p-variational and Lp best approximations and moduli of smoothness. These properties are used to derive the results concerning weighted integrability of Fourier transforms.

Key words and phrases

functions of bounded p-variation approximation by entire functions of exponential type p-variational and Lp moduli of smoothness Fourier transform weighted integrability 

Mathematics Subject Classification

41A17 41A30 42A38 


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The authors thank the referee for useful suggestions and remarks, which improved the revised version of our paper.


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Faculty of Mechanics and MathematicsSaratov State UniversitySaratovRussia

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