L. Xiao

collaborators

2 papers

math.AP2019

Fractional Differential Couples by Sharp Inequalities and Duality Equations

Liguang Li, Jie Xiao

This paper presents a highly non-trivial two-fold study of the fractional differential couples - derivatives ( $\nabla_{+}^{0 < s < 1} = (- Δ)^{\frac{s}{2}}$ ) and gradients ($\nabla^{0<s<1}_-=…

math.AP2019

Intrinsic nature of the Stein-Weiss $H^{1}$ -inequality

Liguang Liu, Jie Xiao

This paper explores the intrinsic nature of the celebrated Stein-Weiss $H^{1}$ -inequality $∥ I_{s} u ∥_{L^{\frac{n}{n - s}}} ≲ ∥ u ∥_{L^{1}} + ∥ R u ∥_{L^{1}} = ∥ u ∥_{H^{1}}$ throu…

Fractional Differential Couples by Sharp Inequalities and Duality Equations

Intrinsic nature of the Stein-Weiss H1-inequality

Intrinsic nature of the Stein-Weiss $H^{1}$ -inequality