本刊英文版2023年66卷第10期(2157–2410)摘要

Sobolev embeddings in infinite dimensions Haimeng Luo,Xu Zhang&Shiliang Zhao Abstract In this paper,we study Sobolev spaces in infinite dimensions and the corresponding embedding the-orems.Our underlying spaces are l"for r∈[1,∞),equipped with corresponding probability measures.For the weighted Sobolev space Wl,pb(l",ra)with a weight a∈er of the Gaussian measure Ya and a gradient weight b∈l∞,we characterize the relation between the weights(a and b)and the continuous(resp.compact)log-Sobolev embedding for p∈[1,∞)(resp.p∈(1,∞)).Several counterexamples are also constructed,which are of independent interest.