Generalized Dyadic Conditions Ensuring the Integrability of Fourier-Walsh Transforms

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