Fractional Sobolev, Moser–Trudinger, Morrey–Sobolev inequalities under Lorentz norms
Fractional Sobolev, Moser–Trudinger, Morrey–Sobolev inequalities under Lorentz norms
复制标题
DOI：
10.1007/s10958-010-9872-6
复制
发表时间：
2010-03
影响因子：
--
通讯作者：
J. Xiao;Zh. Zhai
中科院分区：
文献类型：
--
作者：
J. Xiao;Zh. Zhai
在n> ps，n= ps和n< ps三种情形下，考虑了有界开域上分数阶导数（-△）s/2在Lorentz范数下的Sobolev型不等式，由此建立了分数阶导数在Lorentz范数下的弱型Sobolev不等式，Moser-Trudinger不等式和Morrey-Sobolev不等式.应用这些不等式，我们得到了六个相关的函数不等式的迹形式。书目：44种。
We consider the Sobolev type inequalities under Lorentz norms on bounded open domains for fractional derivatives (−△) s/2 in the following three cases: n> ps, n= ps, and n< ps, whence establishing the weak type Sobolev inequalities, Moser–Trudinger and Morrey–Sobolev inequalities for fractional derivatives in Lorentz norms. Applying these inequalities, we obtain the trace forms of six related functional inequalities. Bibliography: 44 titles.