We consider the Rademacher-and Sobolev-to-Lipschitztype properties for arbitrary quasi-regular strongly local Dirichlet spaces. We discuss the persistence of these properties under localization, globalization, transfer to weighted spaces, tensorization, and direct integration. As byproducts, we obtain: necessary and sufficient conditions to identify a quasi-regular strongly local Dirichlet form on an extended metric topological sigma-finite possibly non-Radon measure space with the Cheeger energy of the space; the tensorization of intrinsic distances; the tensorization of the Varadhan short-time asymptotics. (c) 2025 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/).
Dello Schiavo, L., Suzuki, K. (2025). Persistence of Rademacher-type and Sobolev-to-Lipschitz properties. ADVANCES IN MATHEMATICS, 481 [10.1016/j.aim.2025.110542].
Persistence of Rademacher-type and Sobolev-to-Lipschitz properties
Dello Schiavo L.
;
2025-01-01
Abstract
We consider the Rademacher-and Sobolev-to-Lipschitztype properties for arbitrary quasi-regular strongly local Dirichlet spaces. We discuss the persistence of these properties under localization, globalization, transfer to weighted spaces, tensorization, and direct integration. As byproducts, we obtain: necessary and sufficient conditions to identify a quasi-regular strongly local Dirichlet form on an extended metric topological sigma-finite possibly non-Radon measure space with the Cheeger energy of the space; the tensorization of intrinsic distances; the tensorization of the Varadhan short-time asymptotics. (c) 2025 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/).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
