Parametric two-point integral inequalities for -time differentiable functions with applications.
Partial sums of functions of bounded turning.
Partial sums of functions of bounded turning.
Perturbations of an Ostrowski type inequality and applications.
Petrova elementární metoda vyšetřování Fourierových řad
Poincaré inequalities and dimension free concentration of measure
In this paper, we consider Poincaré inequalities for non-euclidean metrics on ℝd. These inequalities enable us to derive precise dimension free concentration inequalities for product measures. This technique is appropriate for a large scope of concentration rate: between exponential and gaussian and beyond. We give equivalent functional forms of these Poincaré type inequalities in terms of transportation-cost inequalities and inf-convolution inequalities. Workable sufficient conditions are given...
Poincaré inequalities and hitting times
Equivalence of the spectral gap, exponential integrability of hitting times and Lyapunov conditions is well known. We give here the correspondence (with quantitative results) for reversible diffusion processes. As a consequence, we generalize results of Bobkov in the one dimensional case on the value of the Poincaré constant for log-concave measures to superlinear potentials. Finally, we study various functional inequalities under different hitting times integrability conditions (polynomial,…)....
Poincaré inequalities and Sobolev spaces.
Our understanding of the interplay between Poincaré inequalities, Sobolev inequalities and the geometry of the underlying space has changed considerably in recent years. These changes have simultaneously provided new insights into the classical theory and allowed much of that theory to be extended to a wide variety of different settings. This paper reviews some of these new results and techniques and concludes with an example on the preservation of Sobolev spaces by the maximal function.[Proceedings...
Poincaré Inequalities for Mutually Singular Measures
Using an inverse system of metric graphs as in [3], we provide a simple example of a metric space X that admits Poincaré inequalities for a continuum of mutually singular measures.
Poincaré inequalities for the Heisenberg group target.
Poincaré inequalities with Luxemburg norms in -averaging domains.
Poincaré type inequalities for variable exponents.
Pointwise multiplicative inequalities and Nirenberg type estimates in weighted Sobolev spaces
Polynomial Expansions for Solutions of Higher-Order Bessel Heat Equation in Quantum Calculus
Mathematics Subject Class.: 33C10,33D60,26D15,33D05,33D15,33D90In this paper we give the q-analogue of the higher-order Bessel operators studied by I. Dimovski [3],[4], I. Dimovski and V. Kiryakova [5],[6], M. I. Klyuchantsev [17], V. Kiryakova [15], [16], A. Fitouhi, N. H. Mahmoud and S. A. Ould Ahmed Mahmoud [8], and recently by many other authors. Our objective is twofold. First, using the q-Jackson integral and the q-derivative, we aim at establishing some properties of this function with proofs...
Polynomial inequalities for non-commuting operators.
Polynomial inequalities, functional spaces and best approximation on the real semiaxis with Laguerre weights.
Polynomial selections and separation by polynomials
K. Nikodem and the present author proved in [3] a theorem concerning separation by affine functions. Our purpose is to generalize that result for polynomials. As a consequence we obtain two theorems on separation of an n-convex function from an n-concave function by a polynomial of degree at most n and a stability result of Hyers-Ulam type for polynomials.
Polynomials and convex sequence inequalities.
Positive semidefinite matrices, exponential convexity for majorization, and related Cauchy means.
Positive trigonometric sums and applications.