Hardy's inequalities for Hermite and Laguerre expansions revisited
Hardy's inequalities for Hermite and Laguerre expansions revisited
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DOI：
10.2969/jmsj/06330753
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发表时间：
2011-07-01
影响因子：
0.7
通讯作者：
Kanjin, Yuichi
中科院分区：
文献类型：
--
作者：
Kanjin, Yuichi
我们证明了当拉盖尔参数a为正时，拉盖尔展开式的Hardy不等式在空间L-1(0，无穷)上成立，并且证明了当α=0时，该不等式在实Hardy空间H-1(0，无穷)上成立，但在L-1(0，无穷)上不成立。进一步，在L-1(0，无穷)上建立了Hermite展开式的Hardy不等式。
We show that Hardy's inequalities for Laguerre expansions hold on the space L-1(0, infinity) when the Laguerre parameters a are positive, and we prove that although the inequality holds on the real Hardy space H-1(0, infinity) if alpha = 0, it does not hold on L-1(0, infinity). Further, Hardy's inequality for Hermite expansion is established on L-1(0, infinity).