Sharp Hardy-Sobolev inequalities with general weights and remainder terms.
Shift inequalities of Gaussian type and norms of barycentres
We derive the equivalence of different forms of Gaussian type shift inequalities. This completes previous results by Bobkov. Our argument strongly relies on the Gaussian model for which we give a geometric approach in terms of norms of barycentres. Similar inequalities hold in the discrete setting; they improve the known results on the so-called isodiametral problem for the discrete cube. The study of norms of barycentres for subsets of convex bodies completes the exposition.
Small time heat kernel behavior on Riemannian complexes.
Sobolev embeddings with variable exponent
Sobolev inequalities in 2-D hyperbolic space: A borderline case.
Sobolev-type spaces from generalized Poincaré inequalities
We define a Sobolev space by means of a generalized Poincaré inequality and relate it to a corresponding space based on upper gradients.
Solution of one conjecture on inequalities with power-exponential functions.
Some analytical properties of solutions of differential equations of noninteger order.
Some embeddings of weighted Sobolev spaces on finite measure and quasibounded domains.
Some Functional Inequalities.
Some generalization of weighted norm inequalities for certain class of integral operators
Some generalized Poincaré inequalities and applications to problems arising in electromagnetism.
Some Hardy type integral inequalities.
Some inequalities for Sobolev integrals.
Some inequalities obtained by elementary methods
Some integral inequalities of Hardy type
Some integral inequalities of Sturm-Liouville type
Some Landau's type inequalities for infinitesimal generators.
Some new discrete nonlinear delay inequalities and application to discrete delay equations.
Some new Hardy type inequalities and their limiting inequalities.