Sesquiregular Measures in Product Spaces and Convolution of Such Measures
Several discrete inequalities for convex functions.
Several integral inequalities.
Several new perturbed Ostrowski-like type inequalities.
Several refinements and counterparts of Radon's inequality
We establish that the inequality of Radon is a particular case of Jensen's inequality. Starting from several refinements and counterparts of Jensen's inequality by Dragomir and Ionescu, we obtain a counterpart of Radon's inequality. In this way, using a result of Simić we find another counterpart of Radon's inequality. We obtain several applications using Mortici's inequality to improve Hölder's inequality and Liapunov's inequality. To determine the best bounds for some inequalities, we used Matlab...
Sharp constants for Moser-type inequalities concerning embeddings into Zygmund spaces
Let and be a bounded set. We give a Moser-type inequality for an embedding of the Orlicz-Sobolev space , where the Young function behaves like , , for large, into the Zygmund space . We also study the same problem for the embedding of the generalized Lorentz-Sobolev space , , , , embedded into the Zygmund space .
Sharp constants for some inequalities connected to the -Laplace operator.
Sharp error bounds for some quadrature formulae and applications.
Sharp Grüss-type inequalities for functions whose derivatives are of bounded variation.
Sharp Hardy-Sobolev inequalities with general weights and remainder terms.
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.