On the boundedness of non-integer dimension Calder\'on-Zygmund Operators with antisymmetric kernels

Benjamin Jaye; Fedor Nazarov

On the boundedness of non-integer dimension Calder\'on-Zygmund Operators with antisymmetric kernels

Classical Analysis and ODEs 2016-04-08 v1

Authors: Benjamin Jaye , Fedor Nazarov

Abstract

We characterize the non-atomic measures $\mu$ for which all Calder\'{o}n-Zygmund operators with antisymmetric kernels of a fixed non-integer dimension $s$ are bounded in $L^2(\mu)$ in terms of a positive quantity, the Wolff energy.

Keywords

Calderón-Zygmund operators antisymmetric kernels non-integer dimension non-atomic measures L^2 boundedness Wolff energy

Cite

@article{arxiv.1604.02014,
  title  = {On the boundedness of non-integer dimension Calder\'on-Zygmund Operators with antisymmetric kernels},
  author = {Benjamin Jaye and Fedor Nazarov},
  journal= {arXiv preprint arXiv:1604.02014},
  year   = {2016}
}

Comments

20 pages. We have (rather deliberately) imported several definitions from the previous submission arXiv:1602.02821 with minimal changes so that the reader can compare similarities in the methods

On the boundedness of non-integer dimension Calder\'on-Zygmund Operators with antisymmetric kernels

Abstract

Keywords

Cite

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