Variation of the Radon transform (Q1024977)

Estimates are obtained for a variation of the Radon transform. The analysis is motivated in part by Kakeya-Besicovitch sets in the plane. In fact, a problem originally stated by Kakeya was to find a set of smallest area in the plane containing a line segment of unit length in every direction. Besicovitch solved the problem by finding a set of measure 0 having this property. The construction along with some of the history of the problem can be found in the book by \textit{I. J. Schoenberg} [Mathematical time exposures. Washington: The Mathematical Association of America (1982; Zbl 0519.00002)].