Refined limiting imbeddings for Sobolev spaces of vector-valued

摘要

We prove a refined limiting imbedding theorem of the Brezis-Wainger type in the first critical case, i.e. s = N/P, for Sobolev spaces W-p(s) (R-N, E) and Bessel potential spaces H '(RN, E) of functions with values in a general Banach space E. In particular, the space E may lack the UMD property. (c) 2005 Elsevier Inc. All rights reserved.