# Harmonic Measure and the Analyst's Traveling Salesman Theorem

@article{Azzam2019HarmonicMA, title={Harmonic Measure and the Analyst's Traveling Salesman Theorem}, author={Jonas Azzam}, journal={arXiv: Classical Analysis and ODEs}, year={2019} }

We study how generalized Jones $\beta$-numbers relate to harmonic measure. Firstly, we generalize a result of Garnett, Mourgoglou and Tolsa by showing that domains in $\mathbb{R}^{d+1}$ whose boundaries are lower $d$-content regular admit Corona decompositions for harmonic measure if and only if the square sum $\beta_{\partial\Omega}$ of the generalized Jones $\beta$-numbers is finite. Secondly, for semi-uniform domains with Ahlfors regular boundaries, it is known that uniform rectifiability…

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