Geodesic
A Pointwise Estimate for the Fourier Transform and Maxima of a Function
Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 689-696

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DOI

We show a pointwise estimate for the Fourier transform on the line involving the number of times the function changes monotonicity. The contrapositive of the theorem may be used to find a lower bound to the number of local maxima of a function. We also show two applications of the theorem. The first is the two weight problem for the Fourier transform, and the second is estimating the number of roots of the derivative of a function.
DOI : 10.4153/CMB-2011-062-x
Mots-clés : 42A38, 65T99, Fourier transform, maxima, two weight problem, roots, norm estimates, Dirichlet–Jordan theorem 
Berndt, Ryan. A Pointwise Estimate for the Fourier Transform and Maxima of a Function. Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 689-696. doi: 10.4153/CMB-2011-062-x
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