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Mapping properties of integral averaging operators

H. Heinig, G. Sinnamon (1998)

Studia Mathematica

Characterizations are obtained for those pairs of weight functions u and v for which the operators $T f (x) = ʃ_{a (x)}^{b (x)} f (t) d t$ with a and b certain non-negative functions are bounded from $L_{u}^{p} (0, \infty)$ to $L_{v}^{q} (0, \infty)$ , 0 < p,q < ∞, p≥ 1. Sufficient conditions are given for T to be bounded on the cones of monotone functions. The results are applied to give a weighted inequality comparing differences and derivatives as well as a weight characterization for the Steklov operator.

Markov inequalities for polynomials with restricted coefficients.

Cao, Feilong, Lin, Shaobo (2009)

Journal of Inequalities and Applications [electronic only]

Matrix versions of the Cauchy and Kantorovich inequalities.

A.W. Marshall, I. Olkin (1990)

Aequationes mathematicae

Mean values of convexly arranged numbers and monotone rearrangements in reverse integral inequalities

Werner Clemens (2005)

Bollettino dell'Unione Matematica Italiana

We analyse mean values of functions with values in the boundary of a convex two-dimensional set. As an application, reverse integral inequalities imply exactly the same inequalities for the monotone rearrangement. Sharp versions of the classical Gehring lemma, the Gurov-Resetnyak theorem and the Muckenhoupt theorem are obtained.

Measure concentration for compound Poisson distributions.

Kontoyiannis, I., Madiman, M. (2006)

Electronic Communications in Probability [electronic only]

Minimal rearrangements of Sobolev functions

John E. Brothers, William P. Ziemer (1987)

Acta Universitatis Carolinae. Mathematica et Physica

Mixed means for centered and uncentered averaging operators over spheres and related results.

Perić, I. (2008)

Banach Journal of Mathematical Analysis [electronic only]

Moment preserving spline approximation finite intervals and Chakalov-Popoviciu quadratures.

Acu, Ana Maria (2007)

Acta Universitatis Apulensis. Mathematics - Informatics

Moments inequalities of a random variable defined over a finite interval.

Kumar, Pranesh (2002)

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

Monosplines and inequalities for the remainder term of quadrature formulas.

Acu, Ana Maria (2007)

General Mathematics

Monotonic refinements of a Ky Fan inequality.

Chong, K.K. (2001)

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

Monotonicity and convexity of four sequences originating from Nanson's inequality.

Wang, Liang-Cheng (2006)

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

Monotonicity in Banach function spaces

Sinnamon, Gord (2007)

Nonlinear Analysis, Function Spaces and Applications

This paper is an informal presentation of material from [28]–[34]. The monotone envelopes of a function, including the level function, are introduced and their properties are studied. Applications to norm inequalities are given. The down space of a Banach function space is defined and connections are made between monotone envelopes and the norms of the down space and its dual. The connection is shown to be particularly close in the case of universally rearrangement invariant spaces. Next, two equivalent...

Monotonicity of certain functionals under rearrangement

Adriano Garsia, Eugène Rodemich (1974)

Annales de l'institut Fourier

We show here that a wide class of integral inequalities concerning functions on $[0, 1]$ can be obtained by purely combinatorial methods. More precisely, we obtain modulus of continuity or other high order norm estimates for functions satisfying conditions of the type $\int_{0}^{1} \int_{0}^{1} Ψ (\frac{f (x) - f (y)}{p (x - y)}) d x d y < \infty$ where $Ψ (u)$ and $p (u)$ are monotone increasing functions of $| u |$ .Several applications are also derived. In particular these methods are shown to yield a new condition for path continuity of general stochastic processes

Monotonicity of generalized weighted mean values

Alfred Witkowski (2004)

Colloquium Mathematicae

The author gives a new simple proof of monotonicity of the generalized extended mean values $M (r, s) = \leq {((\int f^{s} d μ) / (\int f^{r} d μ))}^{1 / (s - r)}$ introduced by F. Qi.

Monotonicity properties of the relative error of a Padé approximation for Mills' ratio.

Pinelis, Iosif (2002)

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

More about Hermite-Hadamard inequalities, Cauchy's means, and superquadracity.

Abramovich, S., Farid, G., Pečarić, J. (2010)

Journal of Inequalities and Applications [electronic only]

More on inequalities of Simpson type.

Liu, Zheng (2007)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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.

Multidimensional Hilbert-type inequalities with a homogeneous kernel.

Vuković, Predrag (2009)

Journal of Inequalities and Applications [electronic only]

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