ABSTRACT
In this work we show that the Kakeya maximal operator, KN, defined by averages on rectangles of given eccentricity N >> 1 satisfies the weighted inequality https://www.w3.org/1998/Math/MathML">∫R2(KNf)2w≤C(logN)α∫R2|f|2KNw,https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429332838/58f4c041-1317-4a7c-b51a-e794ca13209e/content/eq3881.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
for some constants C and a independent of the function f and the weight w. The motivation for such an inequality comes from the Theory of Bochner–Riesz operators.
