Even singular integral operators that are well behaved on a purely unrectifiable set

We prove the existence of a <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis d minus 2 right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>d</mml:mi> <mml:mo> − </mml:mo> <mml:mn>2</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">(d-2)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -dimensional purely unrectifiable set upon which a family of <italic>even</italic> singular integral operators is bounded.