Some weighted norm inequalities for the Fourier transform of functions with vanishing moments

Sadosky, Cora; Wheeden, Richard L.

doi:10.1090/S0002-9947-1987-0876464-4

Some weighted norm inequalities for the Fourier transform of functions with vanishing moments
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by Cora Sadosky and Richard L. Wheeden

Trans. Amer. Math. Soc. 300 (1987), 521-533

DOI: https://doi.org/10.1090/S0002-9947-1987-0876464-4

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Abstract:

Weighted $L^p$ norm inequalities are derived between a function and its Fourier transform in case the function has vanishing moments up to some order. For weights of the form ${\left | x \right |^\gamma }$, the results concern values of $\gamma$ which are outside the range which is normally considered.

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