Geodesic
Young's integral inequality with upper and lower bounds
Electronic journal of differential equations, Tome 2011 (2011)
Young's integral inequality is reformulated with upper and lower bounds for the remainder. The new inequalities improve Young's integral inequality on all time scales, such that the case where equality holds becomes particularly transparent in this new presentation. The corresponding results for difference equations are given, and several examples are included. We extend these results to piecewise-monotone functions as well.
Classification : 26D15, 39A12, 34N05
Keywords: Young's inequality, monotone functions, Pochhammer lower factorial, difference equations, time scales 
@article{EJDE_2011__2011__a81,
     author = {Anderson,  Douglas R. and Noren,  Steven and Perreault,  Brent},
     title = {Young's integral inequality with upper and lower bounds},
     journal = {Electronic journal of differential equations},
     year = {2011},
     volume = {2011},
     zbl = {1225.26039},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a81/}
}
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AU  - Noren,  Steven
AU  - Perreault,  Brent
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JO  - Electronic journal of differential equations
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VL  - 2011
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%A Noren,  Steven
%A Perreault,  Brent
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%J Electronic journal of differential equations
%D 2011
%V 2011
%U http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a81/
%G en
%F EJDE_2011__2011__a81
Anderson,  Douglas R.; Noren,  Steven; Perreault,  Brent. Young's integral inequality with upper and lower bounds. Electronic journal of differential equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a81/