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Schur multiplier characterization of a class of infinite matrices

A. Marcoci, L. Marcoci, L. E. Persson, N. Popa (2010)

Czechoslovak Mathematical Journal

Let B w ( p ) denote the space of infinite matrices A for which A ( x ) p for all x = { x k } k = 1 p with | x k | 0 . We characterize the upper triangular positive matrices from B w ( p ) , 1 < p < , by using a special kind of Schur multipliers and the G. Bennett factorization technique. Also some related results are stated and discussed.

Several refinements and counterparts of Radon's inequality

Augusta Raţiu, Nicuşor Minculete (2015)

Mathematica Bohemica

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

Robert Černý (2012)

Commentationes Mathematicae Universitatis Carolinae

Let n 2 and Ω n be a bounded set. We give a Moser-type inequality for an embedding of the Orlicz-Sobolev space W 0 L Φ ( Ω ) , where the Young function Φ behaves like t n log α ( t ) , α < n - 1 , for t large, into the Zygmund space Z 0 n - 1 - α n ( Ω ) . We also study the same problem for the embedding of the generalized Lorentz-Sobolev space W 0 m L n m , q log α L ( Ω ) , m < n , q ( 1 , ] , α < 1 q ' , embedded into the Zygmund space Z 0 1 q ' - α ( Ω ) .

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