We prove a fractional version of the logarithmic Hardy–Sobolev inequality on homogeneous Lie groups, which seems new even in the Euclidean setting. As an application, we establish the existence of a weak solution for fractional sub-Laplacians with Hardy potential....
We establish the following Hardy–Littlewood–Sobolev-type inequality: For 0<s<2(\alpha +1),~~1<p<\frac{2(\alpha +1)}{s} and \frac{1}{q}=\frac{1}{p}-\frac{s}{2(\alpha +1)}, there exists a constant C_{\alpha , s, p} such that for all f \in L^{p}([0,+\infty...
FRACTIONAL GAGLIARDO-NIRENBERG INEQUALITY 来自 koreascience.or.kr 喜欢 0 阅读量: 125 作者: YJ Park 摘要: A fractional Gagliardo-Nirenberg inequality is established. A sharp fractional Sobolev inequality is discussed as a direct consequence. 被引量: 8 年份: 2011 ...
We extend a Poincaré-type inequality for functions with large zero-sets by Jiang and Lin to fractional Sobolev spaces. As a consequence, we obtain a Hausdorff dimension estimate on the size of zero-sets for fractional Sobolev functions whose inverse is integrable. Also, for a suboptimal Hausdorf...
本文通过研究分数次积分算子对Orlicz-Hardy空间H_φ(R~n)的作用,引入了势空间H_s~φ(R~n),并给出了其等价刻划,同时证明在一定条件下,当k为整数时,H_k~φ(R~n)等价于Orlicz-Hardy-Sobolev空间H_k~φ(R~n)。 更多例句>> 补充资料:连分数的渐近分数 连分数的渐近分数 convergent of a continued fracti...
We first establish fractional Adams–Moser–Trudinger type inequality on domain Ω⊂Rn with finite measure (Theorem 1.12) and then using this inequality and Hardy–Littlewood–Sobolev inequality adapted to the result of R. O’Neil (1963), we establish singular fractional Adams–Moser–Trudinger typ...
The space (L q ,l p ) α and continuity of the fractional maximal Hardy-Littlewood operator 来自 ResearchGate 喜欢 0 阅读量: 12 作者: I Fofana 摘要: We prove a weak Poincaré-Sobolev type inequality for a function belonging to Morrey spaces with respect to a Hausdorff content....
We establish the optimal asymptotic lower bound for the stability of fractional Sobolev inequality: \begin{equation}\label{Sob sta ine} \left\|(-\Delta)^{s/2} U ight\|_2^2 - \mathcal S_{s,n} \| U\|_{\frac{2n}{n-2s}}^2\geq C_{n,s} d^{2}(U, \mathcal{M}_s), \en...
Sickel, Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations. Walter de Gruyter (1996). MATH Google Scholar J. Sánchez, V. Vergara, A Lyapunov-type inequality for a p-Laplacian operator. Nonlinear Anal. 74, No 18 (2011), 7071–7077. Math...
Introduction A central motivation behind the development of fractional calculus has been the original idea of Leibniz to treat integrals symbolically as negative powers of differentials [1, p. 105], [2] (and [3] for more). Distribution theory [4,5], as well as operational calculus [6,7,8...