Two-Weight Norm Inequalities for the Fourier Transform

摘要: In this short talk we shall give two (trivial) necessary and similar-looking sufficient conditions on non-negative weights V W for the inequality $$ {\smallint _{{R^d}}}{\left| {f(x)} \right|^2}Vdx \leqslant {\hat f(\xi )} \right|^2}Wd\xi $$ (1) to hold all \( f \in C_0^\infty ({R^d}) \) .