Timeline for Reverse Hausdorff Young for nonnegative functions
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 30, 2016 at 6:04 | comment | added | Bill Johnson | The argument works for every infinite dimensional $L_p$ space since every separable $L_p$ space is isometrically isomorphic as a Banach lattice to $X \oplus_p \ell_p^n$ for some $n=0,1,2,\dots, \infty$, where either $X=\{0\}$ or $X=L_p(0,1)$. | |
| Dec 28, 2016 at 18:22 | comment | added | Paata Ivanishvili | Do you consider $L^{p}$ with Lebesgue measure? If not then Nelson's hypercontractivity gives the counterexample. Hermite semigroup $e^{-tH}$ maps $L^{p}(d\gamma)$ into $L^{q}(d\gamma)$ for $1 <p<q<\infty$ where $d\gamma$ is the Gaussian measure. | |
| Oct 7, 2014 at 23:55 | history | answered | Bill Johnson | CC BY-SA 3.0 |