Timeline for Norm of convolution operator
Current License: CC BY-SA 4.0
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| Sep 7, 2019 at 15:47 | comment | added | Marcelo Ng | In some cases, in Harmonic analysis, and in PDE, when we are working whit validity of inequalities we can to construct counter-examples come from "scaling arguments" . In some cases, we use the Schwartz functions because of the nice properties under convolution and Fourier transforms. The Gaussian is used sometimes because we have invariance in relation to Fourier transform and it is a radial function (which is good in Spherical Coordinates). You can found examples in some books as Elias M. Stein or Loukas Grafakos. | |
| Sep 6, 2019 at 18:40 | comment | added | Ayman Moussa | Could you expand a bit ? I am surprised the counter-example comes from a Gaussian as I found some results stating the equivalence when the function is assumed non-negative. | |
| Aug 17, 2019 at 19:01 | history | answered | Marcelo Ng | CC BY-SA 4.0 |