The measures with an associated square function operator bounded in $L^2$

In this paper we provide an extension of a theorem of David and Semmes ('91) to general non-atomic measures. The result provides a geometric characterization of the non-atomic measures for which a certain class of square function operators, or singular integral operators, are bounded in $L^2(μ)$. The description is given in terms of a modification of Jones' $β$-coefficients.

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