, Volume 38, Issue 2, pp 255-278

Pseudodifferential operators on localized Besov spaces

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We study the boundedness of pseudodifferential operators σ(x,D) of order m and symbols σ(x,ξ) 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 pq, we deduce the boundedness of such an operator σ(x,D) on pointwise multipliers Besov space $M(B_{{p},{q}}^{s}({\mathbb{R}}^{n}))$ .