I'm trying to prove global wellposedness for the Klein-Gordon-Equation with **radial** initial data. I'm therefore searching for/trying to prove strichartz estimates of the form: $$ ||e^{it\langle D\rangle}u||_{L^q_{t}L^r_{x}}\lesssim||\langle D\rangle^lu||_{L^{2}}$$ or $$||P_{L}((e^{it\langle D\rangle}u_{M})(e^{it\langle D\rangle}v_{N}))||_{L_{2}}\lesssim L^lM^mN^n||u_{M}||_{L^{2}}||v_{N}||_{L^{2}}$$ with indices $l,m,n$ as small as possible. Where $P_{L}$ is the Littlewoodpaley projector, $e^{it\langle D\rangle}$ the Propagator of the (mass 1) Klein-Gordon-Equation and $L,M,N$ frequencies.

I'm aware, that you have more admissible strichartz exponentens $(q,r)$ for the first kind of estimate if you have radial data (the result is outlined here: http://wiki.math.toronto.edu/DispersiveWiki/index.php/Strichartz_estimates) but I can't see whether/how that can help me since I will get the same $l$ as with none radial data. Am i missing something here?

Also I don't know how to proof the first inequalitity for non-radial-data. I know it is true for $2\leq r<\infty$, $2/q+n/r=n/2$, $l=1/q-1/r+1/2$ and was told to find the proof in Delort and Fang(2000) but I can't. (I hope the proof will help me understand how I can improve the result for radial functions)

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