A Pointwise Estimate for the Fourier Transform and Maxima of a Function

Canadian mathematical bulletin

Ryan Berndt¹ 

[1] Yale University and Otterbein College, Otterbein College, Westerville, Ohio 43081

关键词: Fourier transform;    maxima;    two weight problem;    roots;    norm estimates;    Dirichlet-Jordan theorem;   

DOI  :  10.4153/CMB-2011-062-x

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We show a pointwise estimate for the Fouriertransform on the line involving the number of times the functionchanges monotonicity. The contrapositive of the theorem may be used tofind a lower bound to the number of local maxima of a function. Wealso show two applications of the theorem. The first is the two weightproblem for the Fourier transform, and the second is estimating thenumber of roots of the derivative of a function.

【 授权许可】

Unknown