On certain new Gronwall-Ou-Iang type integral inequalities in two variables and their applications.
On certain new integral inequalities and their applications.
On equivalence of super log Sobolev and Nash type inequalities
We prove the equivalence of Nash type and super log Sobolev inequalities for Dirichlet forms. We also show that both inequalities are equivalent to Orlicz-Sobolev type inequalities. No ultracontractivity of the semigroup is assumed. It is known that there is no equivalence between super log Sobolev or Nash type inequalities and ultracontractivity. We discuss Davies-Simon's counterexample as the borderline case of this equivalence and related open problems.
On functional inequalities in a single variable [Book]
On generalizations of Ostrowski inequality and some related results
Some generalizations of the Ostrowski inequality, the Milovanović-Pečarić-Fink inequality, the Dragomir-Agarwal inequality and the Hadamard inequality are given.
On generalized Moser-Trudinger inequalities without boundary condition
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 -inequalities
Some -analysis variants of Hardy type inequalities of the form with sharp constant 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.
On Hardy type inequality with non-isotropic kernels.
On Hardy's inequality in .
On Heisenberg and local uncertainty principles for the -Dunkl transform.
On inequalities of Hardy-Sobolev type.
On integral inequalities of Gronwall-Bellman-Bihari type in several variables.
On integral inequalities of the Sobolev type.
On jensen type inequalities with ordered variables.
On Lakshmikantham's comparison method for Gronwall inequalities
On Landau type inequalities for functions with Hölder continuous derivatives.
On l'Hospital-type rules for monotonicity.
On maximal overdetermined Hardy's inequality of second order on a finite interval
A characterization of the weighted Hardy inequality Fu 2 C F“v 2, F(0)=F’(0)=F(1)=F’(1)=0 is given.
On Oleck-Opial-Beesack-Troy integro-differential inequalities.
On one-sided BMO and Lipschitz functions