A weighted inequality for the Kakeya maximal operator
A weighted inequality for the Kakeya maximal operator
Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper K Subscript delta"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">K</mml:mi> </mml:mrow> <mml:mi>δ<!-- δ --></mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{\mathcal {K}_\delta }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be the Kakeya Maximal Operator defined as the supremum of averages over parallelepipeds of eccentricity <inline-formula content-type="math/mathml"> <mml:math …