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Title: Sharp conditions for weighted 1-dimensional Poincaré inequalities
Authors: Chua, S.-K. 
Wheeden, R.L.
Keywords: Ap weights
Hardy inequalities
Poincaré inequalities
Sobolev's inequalities
Issue Date: Mar-2000
Source: Chua, S.-K.,Wheeden, R.L. (2000-03). Sharp conditions for weighted 1-dimensional Poincaré inequalities. Indiana University Mathematics Journal 49 (1) : 143-175. ScholarBank@NUS Repository.
Abstract: We obtain necessary and sufficient conditions for all weighted one dimensional Poincaré inequalities. Weighted Hardy-type inequalities are an example of our estimates. We use these estimates to obtain some Poincaré type inequalities on product spaces for product weights. In some cases, we also obtain the exact constants in the inequalities. Finally, we apply our result to study solutions of ordinary differential equations with given average value.
Source Title: Indiana University Mathematics Journal
ISSN: 00222518
Appears in Collections:Staff Publications

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