dimensions $n \geq 3$.

Scope of the paper
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We try to give a full and systematic study of the Strichartz estimates for the KT equation with the known methods to us from the literature. We thus vastly improve the range of the known estimates compared to [@CP], [@KT], in several directions.

1\. We prove all (homogeneous and inhomogeneous) Strichartz estimates for admissible exponents apart from the homogeneous endpoint in $n>1$ and the inhomogeneous double endpoint in $n>1$, see theorem \[thm: Strich admiss\] and the remark thereafter.

2\. We also consider homogeneous estimates for mixed $L^p$-data. For comparison, these estimates correspond to homogeneous estimates for $L^p$-data for the equation. We find their full range in $n=1$ and leave open only some endpoint estimates in higher dimensions.

3\. We apply the techniques of Foschi [@F] to study the inhomogeneous estimates for non-admissible exponents. We find the full range in $n=1$ and leave open some estimates in higher dimensions. An analogous set of estimates is unresolved in the context of the equation too. Note that our result is not contained in the abstract estimates of Taggart [@Tg]. The reason for that is twofold. One is that the real method of interpolation used 