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Exact(17)
This inequality is equivalent to (4.4).
Indeed, this inequality is equivalent to Jensen's inequality (1.9).
This inequality is equivalent to the following (20).
end{aligned} This inequality is equivalent to the one to be proved.
We prove that, under a proper transformation, this inequality is equivalent to the Sobolev inequality in RN.
This inequality is equivalent to (after an elementary manipulation) 8z^{3}- z+1)^{3}zleq(z+1)^{3} sqrt{z^{2}-1}.
Similar(43)
Since the inequality is equivalent to (34).
Using, the inequality is equivalent to, which obviously leads to.
Using the notations and, where and, the inequality is equivalent to, where (5.2). with (5.3).
Using the notations and, where and, the inequality is equivalent to, where (5.8).
For the case where (omegain B^{c}), the inequality is equivalent to bigl 3-2g(2)bigr)e^{2lambda}+bigl 3-5g(2)bigr)e^{lambda}+ bigl 3-2g(2)bigl 3-2g.
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