| Dear Sir, Thanks for your kind reply and references. Indeed the paper you mentioned (Distance sets corresponding to convex bodies ) contains a detailed step by step proof of FKW theorem by Bourgain. However my question was regarding the farther generalization of this theorem in 2-dimension in Bourgain's paper. My question was regarding that. Specifically After proving the FKW theorem he writes (Page 309 last para) as a remark:- \begin{remark} Combined with the results on the spherical maximal function in the plane, Theorem 1 can be improved as follows: \end{remark} \begin{theorem}"\ If $A \subset \R^2$, $\delta(A) >0 $, there exists $l = l(A)$ such that whenever $l_1 > l$ there is a point $x \in A$ fulfilling the condition $\{ |x-y|; y\in A \} \supset [l,l_1] $ \end{theorem} my difficulty is with this part. I would be happy if you could explain the outline of the proof. Thanking you Sincerely Debashish --- On Sat, 7/12/08, Alex Iosevich <iosevich@...> wrote: From: Alex Iosevich <iosevich@...> |
Yahoo! Groups TipsDid you know...Hear how Yahoo! Groups has changed the lives of others. Take me there. |
Having problems with message search?
Fill out this form to ensure your group is one of the first to be migrated to the new message search system.
|
|||||||||||||||||||||||||||
Offline 
Send Email