Timeline for Regularization of Zygmund functions
Current License: CC BY-SA 3.0
4 events
when toggle format | what | by | license | comment | |
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May 22, 2014 at 13:49 | vote | accept | CPJ | ||
May 1, 2011 at 14:23 | comment | added | Andrew | In terms of the first difference Zygmund functions are generally no better than log-Lipschitz as the example for $f$ above shows. Ok, lets do the math. For this $f$ and small $\epsilon>0$ we have $$ \partial_xf_\epsilon(0)=\int_{-1}^1\rho_\epsilon(y)(\log|y|+1)dy= \int_{-\infty}^\infty\rho(y)(\log|\epsilon y|+1)dy= $$ $$ \int_{-\infty}^\infty\rho(y)\log|y|dy+\log\epsilon+1. $$ | |
May 1, 2011 at 13:05 | comment | added | CPJ | But this function is also log-Lipschitz. I know that the estimate on the regularization for such functions is optimal. I would like to know if there is some kernel with which we might get better estimates for Zygmund-functions, just using the Zygmund property. | |
Apr 30, 2011 at 18:06 | history | answered | Andrew | CC BY-SA 3.0 |