Moduli of continuity and average decay of Fourier transforms: two-sided estimates

Details Moduli of continuity and average decay of Fourier transforms: two-sided estimates Moduli of continuity and average decay of Fourier transforms: two-sided estimates

2002-12-18

arxiv.org/abs/math/0212254v3

Mathematics

Classical Analysis and ODEs

15 pages, 1 figure, case of dim=1 added, to appear in: Integable systems, random matrices, and applications: Conference in hon

Scientific paper

We study inequalities between general integral moduli of continuity of a function and the tail integral of its Fourier transform. We obtain, in particular, a refinement of a result due to D. B. H. Cline [2] (Theorem 1.1 below). We note that our approach does not use a regularly varying comparison function as in [2]. A corollary of Theorem 1.1 deals with the equivalence of the two-sided estimates on the modulus of continuity on one hand, and on the tail of the Fourier transform, on the other (Corollary 1.5). This corollary is applied in the proof of the violation of the so-called entropic area law for a critical system of free fermions in [4,5].

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