This paper studies the Hardy-type inequalities on the intervals （may be infinite） with two weights, either vaaishing at two endpoiats of the interval or having mean zero. For the first type of inequalities, in terms...This paper studies the Hardy-type inequalities on the intervals （may be infinite） with two weights, either vaaishing at two endpoiats of the interval or having mean zero. For the first type of inequalities, in terms of new isoperimetric constants, the factor of upper and lower bounds becomes smaller than the known ones. The second type of the inequalities is motivated from probability theory and is new ia the analytic context. The proofs are now rather elementary. Similar improvements are made for Nash inequality, Sobolev-type inequality, and the logarithmic Sobolev inequality on the intervals.展开更多
基金Supported by NSFC(GrantNo.11131003)the"985"project from the Ministry of Education in China
文摘This paper studies the Hardy-type inequalities on the intervals （may be infinite） with two weights, either vaaishing at two endpoiats of the interval or having mean zero. For the first type of inequalities, in terms of new isoperimetric constants, the factor of upper and lower bounds becomes smaller than the known ones. The second type of the inequalities is motivated from probability theory and is new ia the analytic context. The proofs are now rather elementary. Similar improvements are made for Nash inequality, Sobolev-type inequality, and the logarithmic Sobolev inequality on the intervals.
