关于可微函数的一类尖锐伸缩不变不等式
A collection of sharp dilation invariant inequalities for differentiable functions
摘要：
我们在几个涉及函数导数的膨胀不变积分不等式中找到了最佳常数。这些不等式中有些是新的，有些是已知的，没有最佳常数。主要内容：1.估计为梯度的二次型，2。双调和算子的加权Garding不等式，3.带余项的伸缩不变Hardy不等式，4.带尖常数的广义Hardy-Sobolev不等式，5.带尖锐Sobolev余项的Hardy不等式
英文摘要：
We find best constants in several dilation invariant integral inequalities involving derivatives of functions. Some of these inequalities are new and some were known without best constants. The contents: 1. Estimate for a quadratic form of the gradient, 2. Weighted Gårding inequality for the biharmonic operator, 3.Dilation invariant Hardy's inequality with remainder term, 4. Generalized Hardy-Sobolev inequality with sharp constant, 5. Hardy's inequality with sharp Sobolev remainder term.
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