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You can find a complete set of Strichartz estimates for the nonradial KG equation in Lemma 3 in this paper by Machihara, Nakanishi and Ozawa. Let me add that, usually, in proofs of local or global well posedness for the wave or KG equation, the non-endpoint Strichartz estimates are more than enough. Thus the wider range of admissible indices in the radial case is not very helpful in general. It could be useful in some cases in which you expect for some reason a better result for radial data.