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

Robert Černý (2012)

Commentationes Mathematicae Universitatis Carolinae

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 $Z_{0}^{\frac{1}{q^{'}} - α} (Ω)$ .

Sharp error bounds for some quadrature formulae and applications.

Ujević, Nenad (2006)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Sharp Grüss-type inequalities for functions whose derivatives are of bounded variation.

Dragomir, Sever S. (2007)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Sharp Hardy-Sobolev inequalities with general weights and remainder terms.

Shen, Yaotian, Chen, Zhihui (2009)

Journal of Inequalities and Applications [electronic only]

Shift inequalities of Gaussian type and norms of barycentres

F. Barthe, D. Cordero-Erausquin, M. Fradelizi (2001)

Studia Mathematica

We derive the equivalence of different forms of Gaussian type shift inequalities. This completes previous results by Bobkov. Our argument strongly relies on the Gaussian model for which we give a geometric approach in terms of norms of barycentres. Similar inequalities hold in the discrete setting; they improve the known results on the so-called isodiametral problem for the discrete cube. The study of norms of barycentres for subsets of convex bodies completes the exposition.

We define a Sobolev space by means of a generalized Poincaré inequality and relate it to a corresponding space based on upper gradients.

Solution of one conjecture on inequalities with power-exponential functions.

Matejíčka, Ladislav (2009)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Some analytical properties of solutions of differential equations of noninteger order.

Momani, S.M., Hadid, S.B., Alawenh, Z.M. (2004)

International Journal of Mathematics and Mathematical Sciences

Some embeddings of weighted Sobolev spaces on finite measure and quasibounded domains.

Brown, R.C. (1998)

Journal of Inequalities and Applications [electronic only]

Some Functional Inequalities.

Wolfgang Sander (1983)

Monatshefte für Mathematik

Some generalization of weighted norm inequalities for certain class of integral operators

K. Rauf, C. O. Imoru (2002)

Kragujevac Journal of Mathematics

Some generalized Poincaré inequalities and applications to problems arising in electromagnetism.

Nibbi, Roberta (1999)

Journal of Inequalities and Applications [electronic only]

Some Hardy type integral inequalities.

Sarikaya, Mehmet Zeki, Yildirim, Hussein (2006)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Some inequalities for Sobolev integrals.

Dimitrov, Nikolaj, Tersian, Stepan (2009)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Some inequalities obtained by elementary methods

D. D. Adamović, J. E. Pečarić (1983)

Matematički Vesnik

Some integral inequalities of Hardy type

B. Florkiewicz (1980)

Colloquium Mathematicae

Some integral inequalities of Sturm-Liouville type

B. Florkiewicz, A. Rybarski (1976)

Colloquium Mathematicae

Currently displaying 1 – 20 of 42

Page 1 Next

Displaying 1 – 20 of 42

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

Sharp error bounds for some quadrature formulae and applications.

Sharp Grüss-type inequalities for functions whose derivatives are of bounded variation.

Sharp Hardy-Sobolev inequalities with general weights and remainder terms.

Shift inequalities of Gaussian type and norms of barycentres

Small time heat kernel behavior on Riemannian complexes.

Sobolev embeddings with variable exponent

Sobolev inequalities in 2-D hyperbolic space: A borderline case.

Sobolev-type spaces from generalized Poincaré inequalities

Solution of one conjecture on inequalities with power-exponential functions.

Some analytical properties of solutions of differential equations of noninteger order.

Some embeddings of weighted Sobolev spaces on finite measure and quasibounded domains.

Some Functional Inequalities.

Some generalization of weighted norm inequalities for certain class of integral operators

Some generalized Poincaré inequalities and applications to problems arising in electromagnetism.

Some Hardy type integral inequalities.

Some inequalities for Sobolev integrals.

Some inequalities obtained by elementary methods

Some integral inequalities of Hardy type

Some integral inequalities of Sturm-Liouville type

Currently displaying 1 – 20 of 42