论文标题
锥体上整体操作员的规范不平等现象
Norm Inequalities for Integral Operators on Cones
论文作者
论文摘要
在本文中，我们探讨了$ [l^{\ mathrm {p}}，\ l^{q}] $ - 某些积分运算符在圆锥上的某些积分操作员在$ {\ sathbb r}^{n}的加权空间上的有界性。在同质锥体$ v $上。然后将本文的结果应用于重要类的运营商，例如Riemann-Liouville的分数积分运营商，Weyl的分数积分运营商和Laplace的运营商。作为上述特殊情况，我们获得了$ {\ Mathbb r}^{n} $ - 著名的Hardy对阳性领域的不平等现象。我们还证明了双重结果。
In this dissertation we explore the $[L^{\mathrm{p}},\ L^{q}]$-boundedness of certain integral operators on weighted spaces on cones in ${\mathbb R}^{n}.$ These integral operators are of the type $\displaystyle \int_{V}k(x,\ y)f(y)dy$ defined on a homogeneous cone $V$. The results of this dissertation are then applied to an important class of operators such as Riemann-Liouville's fractional integral operators, Weyl's fractional integral operators and Laplace's operators. As special cases of the above, we obtain an ${\mathbb R}^{n}$ -generalization of the celebrated Hardy's inequality on domains of positivity. We also prove dual results.
