%0 Journal Article %T A bound for Mean values of Fourier transforms %A Michel Weber %J Mathematics %D 2011 %I arXiv %X We show that there exists a sequence $\{n_k, k\ge 1\}$ growing at least geometrically such that for any finite non-negative measure $\nu$ such that $\hat \nu\ge 0$, any $T>0$, $$ \int_{-2^{n_k} T}^{2^{n_k} T} \hat \nu(x) \dd x \ll_\e T\,2^{2^{(1+\e)n_k}} \int_\R \Big|{\sin {xT} \over xT} \Big|^{n_k^2} \nu(\dd x). $$ %U http://arxiv.org/abs/1105.3048v1