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Pseudodifferential operators on localized Besov spaces
Madani Moussai
,
Salah Eddine Allaoui
Abstract
We study the boundedness of pseudodifferential operators $\sigma(x,D)$ of order $m$ and symbols $\sigma(x,\xi)$ which satisfy a condition of Dini-type, on localized Besov spaces $(B_{{p},{q}}^{s}({\mathbb{R}}^{n}))_{\ell^{r}}$. In the case $s > n/p$ and $p \le q$, we deduce the boundedness of such an operator $\sigma(x, D)$ on pointwise multipliers Besov space $M(B_{{p},{q}}^{s}({\mathbb{R}}^{n}))$.