Abstract
For a given $p\in(1,\infty)$, we present an example of a Muckenhoupt
weight $w\in A_p$ and a Fourier multiplier $a$ on the weighted Lebesgue space
$L^p(w)$ such that, for any $\tau\in\mathbb{R}\setminus\{0,1\}$, the dilation
of $a$ given by $a_\tau(\xi)=a(\tau\xi)$ is not a Fourier multiplier on
$L^p(w)$.
weight $w\in A_p$ and a Fourier multiplier $a$ on the weighted Lebesgue space
$L^p(w)$ such that, for any $\tau\in\mathbb{R}\setminus\{0,1\}$, the dilation
of $a$ given by $a_\tau(\xi)=a(\tau\xi)$ is not a Fourier multiplier on
$L^p(w)$.
| Original language | English |
|---|---|
| Title of host publication | Analysis without Borders |
| Subtitle of host publication | Advances and Applications |
| Editors | Sergei Rogosin |
| Publisher | Birkhäuser Cham |
| Pages | 109-122 |
| Number of pages | 14 |
| ISBN (Electronic) | 978-3-031-59397-0 |
| ISBN (Print) | 978-3-031-59396-3 |
| DOIs | |
| Publication status | Published - 23 Jul 2024 |
Publication series
| Name | Operator Theory: Advances and Applications |
|---|---|
| Publisher | Birkhäuser Cham |