A remark on the fractional Hardy inequality with a remainder term

作者：Abdellaoui Boumediene^*; Peral Ireneo; Primo Ana

来源：Comptes Rendus Mathematique, 2014, 352(4): 299-303.

DOI：10.1016/j.crma.2014.02.003

We prove in this note the following sharpened fractional Hardy inequality: Let N >= 1, 0 < s < 1, N > 2s, and Omega subset of R-N a bounded domain. Then for all 1 < q < 2, there a positive constant C = C (Omega, q, N, s) such that for all u is an element of C-0(infinity) (Omega)
a(N,S) integral(RN) integral(RN) (u(x) - u(y))(2)/vertical bar x - y vertical bar(N+2s) dxdy -Lambda(N,S) integral(RN) u(2)(x)/vertical bar x vertical bar(2s) dx
>= C(Omega,q,N,s) integral(Omega) integral(Omega) (u(x) - u(y))(2)/vertical bar x - y vertical bar(N+qs) dxdy, (1)
where
a(N,s) = 2(2s-1) pi(-N/2) Gamm

• 出版日期2014-4