Tensorization of p-weak differentiable structures
Eriksson-Bique, Sylvester; Rajala, Tapio; Soultanis, Elefterios (2024-05-07)
Elsevier
07.05.2024
Eriksson-Bique, S., Rajala, T., & Soultanis, E. (2024). Tensorization of p-weak differentiable structures. Journal of Functional Analysis, 287(4), 110497. https://doi.org/10.1016/j.jfa.2024.110497.
https://creativecommons.org/licenses/by/4.0/
© 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
https://creativecommons.org/licenses/by/4.0/
© 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
https://creativecommons.org/licenses/by/4.0/
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:oulu-202408075248
https://urn.fi/URN:NBN:fi:oulu-202408075248
Tiivistelmä
Abstract
We consider p-weak differentiable structures that were recently introduced in [9], and prove that the product of p-weak charts is a p-weak chart. This implies that the product of two spaces with a p-weak differentiable structure also admits a p-weak differentiable structure. We make partial progress on the tensorization problem of Sobolev spaces by showing an isometric embedding result. Further, we establish tensorization when one of the factors is PI.
We consider p-weak differentiable structures that were recently introduced in [9], and prove that the product of p-weak charts is a p-weak chart. This implies that the product of two spaces with a p-weak differentiable structure also admits a p-weak differentiable structure. We make partial progress on the tensorization problem of Sobolev spaces by showing an isometric embedding result. Further, we establish tensorization when one of the factors is PI.
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