Aigerim Kalybay

Summability of a Tchebysheff system of functions

We consider a special type of Tchebysheff systems of functions {ui(⋅)}in=0 and {Vi(⋅)}in=0 defined on the intervals (0, 1] and [1,

A Generalization of the Weighted Hardy Inequality for One Class of Integral Operators

We consider the problem of finding necessary and sufficient conditions for validity of an estimate for a function by some differential operation containing a weight function rather than the ordinary derivative. This operation is referred to as the ρ-weighted derivative.

Boundedness of -Multiple Discrete Hardy Operators with Weights for

We find necessary and sufficient conditions on weighted sequences , , , and , for which the operator is bounded from to for .

One-dimensional differential Hardy inequality

We establish necessary and sufficient conditions for the one-dimensional differential Hardy inequality to hold, including the overdetermined case. The solution is given in terms different from those of the known results. Moreover, the least constant for this inequality is estimated.

An extended discrete weighted Hardy inequality in the difference form

In the paper we study some extension of the discrete Hardy inequality written in the difference form, namely “three-weighted Hardy type inequality”. We also obtain a new estimate of the best constant of this inequality.

Weighted Estimates of a Class of Integral Operators with Three Parameters

We characterize the validity of a Hardy-type inequality with a kernel and three parameters under some conditions on three weight functions , , and .

Three weights higher order Hardy type inequalities

We investigate the following three weights higher order Hardy type inequality (0.1) ‖g‖q,u≤  C‖Dρkg‖p,v where Dρi denotes the following weighted differential operator: {dig(t)dti,i=0,1,...,m−1,di−mdti−m(p(t)dmg(t)dtm),i=m,m