A bound for Mean values of Fourier transforms

Details A bound for Mean values of Fourier transforms A bound for Mean values of Fourier transforms

2011-05-16

arxiv.org/abs/1105.3048v1

Mathematics

Functional Analysis

Scientific paper

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 $T>0$, $$ \int_{-2^{n_k} T}^{2^{n_k} T} \hat \nu(x) \dd x
\ll_\e T\,2^{2^{(1+\e)n_k}} \int_\R \Big|{\sin {xT} \over xT} \Big|^{n_k^2}
\nu(\dd x). $$

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