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On generalized Moser-Trudinger inequalities without boundary condition

Robert Černý (2012)

Czechoslovak Mathematical Journal

We give a version of the Moser-Trudinger inequality without boundary condition for Orlicz-Sobolev spaces embedded into exponential and multiple exponential spaces. We also derive the Concentration-Compactness Alternative for this inequality. As an application of our Concentration-Compactness Alternative we prove that a functional with the sub-critical growth attains its maximum.

On Hardy q -inequalities

Lech Maligranda, Ryskul Oinarov, Lars-Erik Persson (2014)

Czechoslovak Mathematical Journal

Some q -analysis variants of Hardy type inequalities of the form 0 b x α - 1 0 x t - α f ( t ) d q t p d q x C 0 b f p ( t ) d q t with sharp constant C are proved and discussed. A similar result with the Riemann-Liouville operator involved is also proved. Finally, it is pointed out that by using these techniques we can also obtain some new discrete Hardy and Copson type inequalities in the classical case.

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