Ron Kerman

Weighted norm inequalities for operators of Hardy type

A new proof, yielding new conditions, is given for the two-weighted norm Hardy inequality. The theorem is extended to operators with kernels behaving much like the Riemann-Liouville fractional integrals of nonnegative order

ERROR ESTIMATES FOR DOMINICI’S HERMITE FUNCTION ASYMPTOTIC FORMULA AND SOME APPLICATIONS

The aim of this paper is to find a concrete bound for the error involved when approximating the nth Hermite function (in the oscillating range) by an asymptotic formula due to D. Dominici. This bound is then used to study the accuracy of certain approximations to Hermite expansions and to Fourier transforms. A way of estimating an unknown probability density is proposed.

Weight structure theorems and factorization of positive operators

We characterize the conditions under which weighted norm inequalities for a positive operator T can be obtained by interpolation with change of measure. The results are applied to the construction of all good weight pairs for T. This construction is used to show that the study of weighted norm inequalities for operators T that factor as T = PQ reduce to that of the weighted norm inequalities for the factors P and Q.

A new algorithm for approximating the least concave majorant

The least concave majorant,

Weighted

\hat F

integral inequalities for operators of Hardy type

F^, of a continuous function F on a closed interval, I, is defined by

Remainder estimates for the approximation numbers of weighted Hardy operators acting onL2

\hat F\left( x \right) = \inf \left\{ {G\left( x \right):G \geqslant F,Gconcave} \right\},x \in I.