Sharp inequalities for periodic functions.
Sharp integral inequalities for products of convex functions.
Sharp integral inequalities involving high-order partial derivatives.
Sharp -weighted Sobolev inequalities
We prove sharp weighted inequalities of the formwhere is a differential operator and is a combination of maximal type operator related to and to .
Sharpening and generalizations of Shafer's inequality for the arc tangent function.
Sharpening of Jordan's inequality and its applications.
Sharpening the Becker-Stark inequalities.
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.
Short proofs of some inequalities of Horst Alzer
We provide elementary proofs of some inequalities of Horst Alzer.
Simmetrizzazione e disuguaglianze di tipo Pòlya-Szegö
Si presentano alcuni risultati recenti riguardanti la disuguaglianza di Pòlya- Szegö e la caratterizzazione dei casi in cui essa si riduce ad un'uguaglianza. Particolare attenzione viene rivolta alla simmetrizzazione di Steiner di insiemi di perimetro finito e di funzioni di Sobolev.
Small time heat kernel behavior on Riemannian complexes.
Sobolev and isoperimetric inequalities for degenerate metrics.
Sobolev embeddings with variable exponent
Sobolev inequalities for probability measures on the real line
We give a characterization of those probability measures on the real line which satisfy certain Sobolev inequalities. Our starting point is a simpler approach to the Bobkov-Götze characterization of measures satisfying a logarithmic Sobolev inequality. As an application of the criterion we present a soft proof of the Latała-Oleszkiewicz inequality for exponential measures, and describe the measures on the line which have the same property. New concentration inequalities for product measures follow....
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 applications of the Briot-Bouquet differential subordination.
Some aspects of convex functions and their applications.