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3 votes
0 answers
308 views

Question on estimate in one of Jean Bourgain's 1992 papers

The paper in question is A Remark on Schrodinger Operators. The goal of the argument is to estimate the following integral: $$K_1(x,y)=\int_{\mathbb{R}^2} e^{i(x-y)\cdot\xi+i(t(x)-t(y))|\xi|^2}\...
Dispersion's user avatar
9 votes
2 answers
628 views

How was Claim 5 in "A non-linear generalisation of the Loomis–Whitney inequality and applications" thought up?

In Bennett, Carbery and Wright's paper A non-linear generalisation of the Loomis–Whitney inequality and applications, Claim 5 was used to generalise the case from characteristic functions to simple ...
enihcamemit's user avatar
2 votes
2 answers
917 views

Decay of the Fourier transform of a non-differentiable function

It is well known that if $\varphi$ is a Schwartz function on $\mathbb{R}$ (i.e. smooth and decaying at infinity faster than polynomials), then its Fourier transform decays faster than polynomials. ...
Tony419's user avatar
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