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
P-Adic Numbers Ultrametric Analysis and Applications
Université Ibn Zohr
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Othman Tyr (Wed,) studied this question.
www.synapsesocial.com/papers/69fd7ee0bfa21ec5bbf07296 — DOI: https://doi.org/10.1134/s2070046626020044