English

A Note On $\ell^r$-Valued Calderon-Zygmund Operators

Classical Analysis and ODEs 2012-10-29 v1

Abstract

We consider r\ell^r extensions of Calderon-Zygmund operators on weighted spaces Lp(w)L^p(w) with ww an ApA_p weight and 1<p<1 < p < \infty. We give quantitative estimates of these operators' norm in terms of a given weight's ApA_p characteristic. In particular, using a decomposition theorem of A. Lerner, we show that these extensions recover certain scalar estimates. Related results on general Banach spaces have been studied by Hytonen and Hannien.

Keywords

Cite

@article{arxiv.1210.7025,
  title  = {A Note On $\ell^r$-Valued Calderon-Zygmund Operators},
  author = {James Scurry},
  journal= {arXiv preprint arXiv:1210.7025},
  year   = {2012}
}