S. N. Bernstein type estimations in the mean on the curves in a complex plane.
Let denote the space of infinite matrices for which for all with . We characterize the upper triangular positive matrices from , , by using a special kind of Schur multipliers and the G. Bennett factorization technique. Also some related results are stated and discussed.
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...
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 .