$L^1$中的Dirac-Hardy和Dirac-Sobolev不等式
The Dirac-Hardy and Dirac-Sobolev inequalities in $L^1$
摘要：
建立了$L^1$中的Dirac-Sobolev和Dirac-Hardy不等式，其中用弱$L^p$空间代替了经典Sobolev和Hardy不等式中的$L^p$空间.对Loss和Yau构造的适当Pauli算子的零模给出了与经典不等式类似的反例。
英文摘要：
Dirac-Sobolev and Dirac-Hardy inequalities in $L^1$ are established in which the $L^p$ spaces which feature in the classical Sobolev and Hardy inequalities are replaced by weak $L^p$ spaces. Counter examples to the analogues of the classical inequalities are shown to be provided by zero modes for appropriate Pauli operators constructed by Loss and Yau.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
