Acta Mathematica Vietnamica

, Volume 38, Issue 2, pp 255–278

Pseudodifferential operators on localized Besov spaces

Article

DOI: 10.1007/s40306-013-0019-y

Cite this article as:
Moussai, M. & Allaoui, S.E. Acta Math Vietnam. (2013) 38: 255. doi:10.1007/s40306-013-0019-y
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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 pq, we deduce the boundedness of such an operator σ(x,D) on pointwise multipliers Besov space \(M(B_{{p},{q}}^{s}({\mathbb{R}}^{n}))\).

Keywords

Pseudodifferential operators Besov spaces Localized Besov spaces Pointwise multipliers spaces 

Mathematics Subject Classification (2000)

47E38 47G30 

Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2013

Authors and Affiliations

  1. 1.Department of Mathematics, LAFGEUniversity of M’SilaM’SilaAlgeria
  2. 2.Department of MathematicsUniversity of BatnaBatnaAlgeria

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