Taiwanese Journal of Mathematics


Pengtao Li and Zhichun Zhai

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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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Taiwanese J. Math., Volume 15, Number 5 (2011), 2043-2058.

First available in Project Euclid: 18 July 2017

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Primary: 42B35: Function spaces arising in harmonic analysis 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 26D07: Inequalities involving other types of functions

$Q-$spaces John-Nirenberg inequality Trudinger-Moser inequality


Li, Pengtao; Zhai, Zhichun. SEVERAL ANALYTIC INEQUALITIES IN SOME Q−SPACES. Taiwanese J. Math. 15 (2011), no. 5, 2043--2058. doi:10.11650/twjm/1500406422. https://projecteuclid.org/euclid.twjm/1500406422

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