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Boundedness of the square function and rectifiability

Classical Analysis and ODEs 2009-09-01 v1 Functional Analysis
Authors: Svitlana Mayboroda , Alexander Volberg
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Abstract

Following a recent paper by X. Tolsa [JFA, 2008] we show that the finiteness of square function associated with the Riesz transforms with respect to Hausdorff measure HnH^n (nn is interger) on a set EE implies that EE is rectifiable.

Keywords

hausdorff measure and dimension fourier analysis function spaces and inequalities

Cite

@article{arxiv.0906.2664,
  title  = {Boundedness of the square function and rectifiability},
  author = {Svitlana Mayboroda and Alexander Volberg},
  journal= {arXiv preprint arXiv:0906.2664},
  year   = {2009}
}

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