A note on Ostrowski like inequalities.
A note on Ostrowski like inequalities in spaces.
A note on the Poincaré inequality
The Poincaré inequality is extended to uniformly doubling metric-measure spaces which satisfy a version of the triangle comparison property. The proof is based on a generalization of the change of variables formula.
A pointwise estimate for the solution to a linear Volterra integral equation
Utilizzando una generalizzazione della disuguaglianza di Gronwall si fornisce una stima puntuale per la soluzione dell’equazione lineare integrale di Volterra di seconda specie. Tale stima può essere applicata utilmente anche nello studio della stabilità di equazioni di evoluzione per mezzi continui.
A refinement of the Poincaré inequality for Kolmogorov operators on .
A reversed Poincaré inequality for monotone functions.
A review of selected topics in majorization theory
In this expository paper, some recent developments in majorization theory are reviewed. Selected topics on group majorizations, group-induced cone orderings, Eaton triples, normal decomposition systems and similarly separable vectors are discussed. Special attention is devoted to majorization inequalities. A unified approach is presented for proving majorization relations for eigenvalues and singular values of matrices. Some methods based on the Chebyshev functional and similarly separable vectors...
A sequence of mappings associated with the Hermite-Hadamard inequalities and applications
New properties for some sequences of functions defined by multiple integrals associated with the Hermite-Hadamard integral inequality for convex functions and some applications are given.
A sharp rearrangement inequality for the fractional maximal operator
We prove a sharp pointwise estimate of the nonincreasing rearrangement of the fractional maximal function of ⨍, , by an expression involving the nonincreasing rearrangement of ⨍. This estimate is used to obtain necessary and sufficient conditions for the boundedness of between classical Lorentz spaces.
A sharp weighted Wirtinger inequality
We obtain a sharp estimate for the best constant in the Wirtinger type inequality where is bounded above and below away from zero, is -periodic and such that , and . Our result generalizes an inequality of Piccinini and Spagnolo.
A simple proof of the Chui-Smith theorem on Landau's problem
A simple proof of the Poincaré inequality for a large class of probability measures.
A Sobolev-type inequality with applications.
A study of some constants characterizing the weighted Hardy inequality
A study on some new types of Hardy-Hilbert's integral inequality.
A sufficient condition for the integral version of Martins' inequality.
A survey on Cauchy-Bunyakovsky-Schwarz type discrete inequalities.
A theory on perturbations of the Dirac operator.
A two-weight inequality for the Bessel potential operator
Necessary conditions and sufficient conditions are derived in order that Bessel potential operator is bounded from the weighted Lebesgue spaces into when .
A unified approach to several inequalities involving functions and derivatives
There are many inequalities measuring the deviation of the average of a function over an interval from a linear combination of values of the function and some of its derivatives. A general setting is given from which the desired inequalities are obtained using Hölder’s inequality. Moreover, sharpness of the constants is usually easy to prove by studying the equality cases of Hölder’s inequality. Comparison of averages, extension to weighted integrals and -dimensional results are also given.