Evaluates the integrability of Fourier-Walsh transforms in Lebesgue space functions, highlighting theoretical significance.
Sufficient dyadic conditions are obtained for functions in the Lebesgue space Lᵖ([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.
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