Non-smooth atomic decompositions, traces on Lipschitz domains, and pointwise multipliers in function spaces

Cornelia Schneider; Jan Vybíral

Non-smooth atomic decompositions, traces on Lipschitz domains, and pointwise multipliers in function spaces

Functional Analysis 2012-01-12 v1

Authors: Cornelia Schneider , Jan Vybíral

Abstract

We provide non-smooth atomic decompositions for Besov spaces $\Bd(\rn)$ , $s>0$ , $0<p,q\leq \infty$ , defined via differences. The results are used to compute the trace of Besov spaces on the boundary $\Gamma$ of bounded Lipschitz domains $\Omega$ with smoothness $s$ restricted to $0<s<1$ and no further restrictions on the parameters $p,q$ . We conclude with some more applications in terms of pointwise multipliers.

Keywords

non-smooth atomic decompositions Besov spaces traces on Lipschitz domains pointwise multipliers function spaces

Cite

@article{arxiv.1201.2280,
  title  = {Non-smooth atomic decompositions, traces on Lipschitz domains, and pointwise multipliers in function spaces},
  author = {Cornelia Schneider and Jan Vybíral},
  journal= {arXiv preprint arXiv:1201.2280},
  year   = {2012}
}

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