Abstract
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 p≤q, we deduce the boundedness of such an operator σ(x,D) on pointwise multipliers Besov space \(M(B_{{p},{q}}^{s}({\mathbb{R}}^{n}))\).
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We would like to thank the referee for his remarks, which led to an improvement of the paper.
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Moussai, M., Allaoui, S.E. Pseudodifferential operators on localized Besov spaces. Acta Math Vietnam. 38, 255–278 (2013). https://doi.org/10.1007/s40306-013-0019-y
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DOI: https://doi.org/10.1007/s40306-013-0019-y