Note on the concentration-compactness principle for generalized Moser-Trudinger inequalities

Robert Černý

Displaying similar documents to “Note on the concentration-compactness principle for generalized Moser-Trudinger inequalities”

Sharp generalized Trudinger inequalities via truncation for embedding into multiple exponential spaces

Robert Černý (2010)

Commentationes Mathematicae Universitatis Carolinae

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We prove that the generalized Trudinger inequality for Orlicz-Sobolev spaces embedded into multiple exponential spaces implies a version of an inequality due to Brézis and Wainger.

On generalized Moser-Trudinger inequalities without boundary condition

Robert Černý (2012)

Czechoslovak Mathematical Journal

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We give a version of the Moser-Trudinger inequality without boundary condition for Orlicz-Sobolev spaces embedded into exponential and multiple exponential spaces. We also derive the Concentration-Compactness Alternative for this inequality. As an application of our Concentration-Compactness Alternative we prove that a functional with the sub-critical growth attains its maximum.

Sharp constants for Moser-type inequalities concerning embeddings into Zygmund spaces

Robert Černý (2012)

Commentationes Mathematicae Universitatis Carolinae

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Let $n \geq 2$ and $Ω \subset ℝ^{n}$ 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 $Z_{0}^{\frac{n - 1 - α}{n}} (Ω)$ . We also study the same problem for the embedding of the generalized Lorentz-Sobolev space $W_{0}^{m} L^{\frac{n}{m}, q} {log}^{α} L (Ω)$ , $m < n$ , $q \in (1, \infty]$ , $α < \frac{1}{q^{'}}$ , embedded into the Zygmund space $Z_{0}^{\frac{1}{q^{'}} - α} (Ω)$ .

Decomposition and Moser's lemma.

David E. Edmunds, Miroslav Krbec (2002)

Revista Matemática Complutense

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Using the idea of the optimal decomposition developed in recent papers (Edmunds-Krbec, 2000) and in Cruz-Uribe-Krbec we study the boundedness of the operator Tg(x) = ∫ g(u)du / u, x ∈ (0,1), and its logarithmic variant between Lorentz spaces and exponential Orlicz and Lorentz-Orlicz spaces. These operators are naturally linked with Moser's lemma, O'Neil's convolution inequality, and estimates for functions with prescribed rearrangement. We give sufficient conditions for...