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May 8, 2026P-Adic Numbers Ultrametric Analysis and Applications0 citations

Generalized Dyadic Conditions Ensuring the Integrability of Fourier-Walsh Transforms

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OTOthman Tyr

Key Points

  • The aim is to establish sufficient dyadic conditions for the integrability of Fourier-Walsh transforms in Lebesgue spaces.
  • Derived conditions using moduli of smoothness for functions in Lebesgue space
  • Assessed integrability for functions in L^p([0, +∞)) where 1≤p≤2
  • Established dyadic conditions ensure integrability of Fourier-Walsh transforms for specified functions
  • Conditions were shown to be sharp and confirm existing results by Platonov

Abstract

Sufficient dyadic conditions are obtained for functions in the Lebesgue space L^p ([0, +) ) with 1 p 2, ensuring the integrability of their Fourier-Walsh transforms. These conditions are expressed in terms of moduli of smoothness and are shown to be sharp. As a result, a recent result established by Platonov in this framework is deduced.

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Othman Tyr (2026) studied this question.

synapsesocial.com/papers/69fd7ee0bfa21ec5bbf07296https://doi.org/10.1134/s2070046626020044
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