Several analytic inequalities in some $Q-$spaces

Details Several analytic inequalities in some $Q-$spaces Several analytic inequalities in some $Q-$spaces

2009-04-23

arxiv.org/abs/0904.3768v2

Mathematics

Analysis of PDEs

13 pages submitted

Scientific paper

In this paper, we establish separate necessary and sufficient John-Nirenberg (JN) type inequalities for functions in $Q_{\alpha}^{\beta}(\mathbb{R}^{n})$ which imply Gagliardo-Nirenberg (GN) type inequalities in $Q_{\alpha}(\mathbb{R}^{n}).$ Consequently, we obtain Trudinger-Moser type inequalities and Brezis-Gallouet-Wainger type inequalities in $Q_{\alpha}(\mathbb{R}^{n}).$

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