Inserted: 10 dec 2015
Last Updated: 18 may 2017
With respect to the previous version, we improved the presentation and corrected few typos
We study the structure of Sobolev spaces on the cartesian and 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.