Journal of Mathematical Analysis and Applications
Weight Functions, Fourier Transform
We discuss conditions on weight functions, necessary or sufficient, so that the Fourier transform is bounded from one weighted Lebesgue space to another. The sufficient condition and the primary necessary condition presented are similar, one being phrased is terms of arbitrary measurable sets and the other in terms of cubes. We believe that the symmetry amongst the two conditions helps frame how a single condition, necessary and sufficient, might appear.
Berndt, Ryan, "Symmetric Conditions for a Weighted Fourier Transform Inequality" (2011). Mathematics Faculty Scholarship. 11.
Berndt, R. "Symmetric Conditions For A Weighted Fourier Transform Inequality." Journal Of Mathematical Analysis And Applications 379.1 (2011): 439-443.