Sobolev spaces on warped products

We study the structure of Sobolev spaces on the cartesian/warped products of a given metric measure space and an interval. Our main results are: – the characterization of the Sobolev spaces in such products,– the proof that, under natural assumptions, the warped products possess the Sobolev-to-Lipschitz property, which is key for geometric applications.The results of this paper have been needed in the recent proof of the ‘volume-cone-to-metric-cone’ property of RCD spaces obtained by the first author and De Philippis.