AN EMBEDDING THEOREM

作者：Chernyavskaya N A^*; Shuster L A

来源：Proceedings of the American Mathematical Society, 2013, 141(9): 3213-3221.

DOI：10.1090/S0002-9939-2013-11805-8

We consider a weighted space W (2) 1 (R, q) of Sobolev type: W-1((2)) 1 (R, q) - y is an element of AC ((1))(loc) (R) : broken vertical bar broken vertical bar y%26quot; broken vertical bar broken vertical bar L-1(R) + broken vertical bar broken vertical bar qy broken vertical bar broken vertical bar L-1(R) %26lt; infinity, where 0 %26lt;= q is an element of L-1(loc) (R) and broken vertical bar broken vertical bar y broken vertical bar broken vertical bar W-1 ((2)) 1 (R, q) = broken vertical bar broken vertical bar y broken vertical bar broken vertical bar L1(R) + broken vertical bar broken vertical bar qy broken vertical bar broken vertical bar L-1(R). We obtain a precise condition which guarantees the embedding W-1((2)) 1 (R, q) hooked right arrow L-p(R), p is an element of [1,infinity).

• 出版日期2013-9