A trace law for the Hardy-Morrey-Sobolev space

作者：Liu, L.; Xiao, J.^*

来源：Journal of Functional Analysis, 2018, 274(1): 80-120.

DOI：10.1016/j.jfa.2017.10.004

• Riesz-Hardy-Morrey potential
• Hardy-Morrey-Radon space
• Trace law

This article shows that if HLp,k and HL mu q,lambda are (p, k)-Hardy-Morrey space based on the standard Lebesgue measure and (q, lambda)-Hardy-Morrey space induced by the non -negative Radon measure mu respectively then one has the following trace law for the Hardy-Morrey-Sobolev space I-alpha(HLp,k) of Riesz potentials of order alpha of HLp,k-functions:
sup(0 < parallel to f parallel to HLp,k < infinity) parallel to I(alpha)f parallel to HL mu q,lambda parallel to f parallel to(-1)(HLp,k) < infinity
double left right arrow sup((x, r) is an element of Rn x (0, infinity)) r(-beta) mu(B(x, r)) < infinity
under
{0 < lambda <= k <= n;
0 < alpha < n;
0 < p < k/alpha;
n - alpha p < beta <= n;
0 < q = p(beta + lambda - n)/(k - alpha P).

• 出版日期2018-1-1
• 单位中国人民大学