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An eigenvalue problem related to Hardy’s $L^{P}$ inequality

Moshe Marcus; Itai Shafrir — 2000

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Moser-Trudinger and logarithmic HLS inequalities for systems

Itai Shafrir; Gershon Wolansky — 2005

Journal of the European Mathematical Society

We prove several optimal Moser–Trudinger and logarithmic Hardy–Littlewood–Sobolev inequalities for systems in two dimensions. These include inequalities on the sphere $S^{2}$ , on a bounded domain $Ω \subset ℝ^{2}$ and on all of $ℝ^{2}$ . In some cases we also address the question of existence of minimizers.

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An eigenvalue problem related to Hardy’s L P inequality

Moser-Trudinger and logarithmic HLS inequalities for systems

An eigenvalue problem related to Hardy’s $L^{P}$ inequality