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

Robert Černý

Displaying similar documents to “Sharp constants for Moser-type inequalities concerning embeddings into Zygmund spaces”

Superposition of imbeddings and Fefferman's inequality

Miroslav Krbec, Thomas Schott (1999)

Bollettino dell'Unione Matematica Italiana

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In questo lavoro si studiano condizioni sufficienti sulla funzione peso $V$ , espresse in termini di integrabilità, per la validità della disuguaglianza ${(\int_{B} u^{2} (x) V (x) d x)}^{\frac{1}{2}} \leq c {(\int_{B} {(\nabla u (x))}^{2} d x)}^{\frac{1}{2}},$ dove $B$ denota una sfera in $R^{N}$ . Usando una tecnica di decomposizione di immersioni si dimostrano condizioni sufficienti in termini di appartenenza a spazi di Lebesgue, Lorentz-Orlicz e/o di tipo debole. Come applicazioni vengono fornite condizioni sufficienti per la proprietà forte di prolungamento unico per $|Δ u| \leq V |u|$ nelle dimensioni 2 e 3. ...

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.

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...

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

Robert Černý (2012)

Open Mathematics

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Let Ω ⊂ ℝn, n ≥ 2, be a bounded domain and let α < n − 1. Motivated by Theorem I.6 and Remark I.18 of [Lions P.-L., The concentration-compactness principle in the calculus of variations. The limit case. I, Rev. Mat. Iberoamericana, 1985, 1(1), 145–201] and by the results of [Černý R., Cianchi A., Hencl S., Concentration-Compactness Principle for Moser-Trudinger inequalities: new results and proofs, Ann. Mat. Pura Appl. (in press), DOI: 10.1007/s10231-011-0220-3], we give a sharp estimate...

Hardy-Sobolev Inequalities for Hessian Integrals

Nunzia Gavitone (2007)

Bollettino dell'Unione Matematica Italiana

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Using appropriate symmetrization arguments, we prove the Hardy-Sobolev type inequalities for Hessian Integrals which extend the classical results, well known for Sobolev functions. For such inequalities the value of the best constant is given. Finally we give an improvement of these inequalities by adding a second term that, involves another singular weight which is a suitable negative power of $\log(|x|)$ .

Mappings with dilatation in Orlicz spaces.

Jana Björn (2002)

Collectanea Mathematica

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On equivalence of super log Sobolev and Nash type inequalities

Marco Biroli, Patrick Maheux (2014)

Colloquium Mathematicae

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We prove the equivalence of Nash type and super log Sobolev inequalities for Dirichlet forms. We also show that both inequalities are equivalent to Orlicz-Sobolev type inequalities. No ultracontractivity of the semigroup is assumed. It is known that there is no equivalence between super log Sobolev or Nash type inequalities and ultracontractivity. We discuss Davies-Simon's counterexample as the borderline case of this equivalence and related open problems.