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A walk through nonstandard analysis on the paths of A. Robinson. (Balade en analyse non standard sur les traces de A. Robinson.)

Pétry, André (1996)

Bulletin of the Belgian Mathematical Society - Simon Stevin

A weighted estimate for an intermediate operator on the cone of nonnegative functions.

Oinarov, Ryskul (2002)

Sibirskij Matematicheskij Zhurnal

A weighted inequality for derivatives on the half-line.

Kilgore, T. (1997)

Journal of Inequalities and Applications [electronic only]

A weighted inequality for the Hardy operator involving suprema

Pavla Hofmanová (2016)

Commentationes Mathematicae Universitatis Carolinae

Let $u$ be a weight on $(0, \infty)$ . Assume that $u$ is continuous on $(0, \infty)$ . Let the operator $S_{u}$ be given at measurable non-negative function $ϕ$ on $(0, \infty)$ by $S_{u} ϕ (t) = sup_{0 < τ \leq t} u (τ) ϕ (τ) .$ We characterize weights $v, w$ on $(0, \infty)$ for which there exists a positive constant $C$ such that the inequality ${(\int_{0}^{\infty} {[S_{u} ϕ (t)]}^{q} w (t) d t)}^{\frac{1}{q}} ≲ {(\int_{0}^{\infty} {[ϕ (t)]}^{p} v (t) d t)}^{\frac{1}{p}}$ holds for every $0 < p, q < \infty$ . Such inequalities have been used in the study of optimal Sobolev embeddings and boundedness of certain operators on classical Lorenz spaces.

A weighted isoperimetric inequality and applications to symmetrization.

Betta, M.F., Brock, F., Mercaldo, A., Possteraro, M.R. (1999)

Journal of Inequalities and Applications [electronic only]

A well-rounded linear function.

Eggleton, Roger B. (2001)

The Electronic Journal of Combinatorics [electronic only]

A $σ$ -porous set need not be $σ$ -bilaterally porous

R. J. Nájares, Luděk Zajíček (1994)

Commentationes Mathematicae Universitatis Carolinae

A closed subset of the real line which is right porous but is not $σ$ -left-porous is constructed.

Abel's equation and regular growth: Variations on a theme by Abel.

Szekeres, George (1998)

Experimental Mathematics

About a man and lions

V. Janković (1978)

Matematički Vesnik

About a non-homogeneous Hardy-inequality and its relation with the spectrum of Dirac operators

Jean Dolbeault, Maria J. Esteban, Eric Séré (2001/2002)

Séminaire Équations aux dérivées partielles

A non-homogeneous Hardy-like inequality has recently been found to be closely related to the knowledge of the lowest eigenvalue of a large class of Dirac operators in the gap of their continuous spectrum.