Upper bounds for Stein-type operators

Error bounds in approximating n-time differentiable functions of self-adjoint operators in Hilbert spaces via a Taylor's type expansion

On utilizing the spectral representation of selfadjoint operators in Hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in Hilbert Spaces via a Taylor's type expansion are given.

Maximal operators: scales, curvature and the fractal dimension

We establish L bounds for the Bourgain-Stein spherical maximal operator in the setting of compactly supported Borel measures μ, ν satisfying natural local size assumptions μ(B(x, r)) ≤ Crμ , ν(B(x, r)) ≤ Crν . Taking the supremum over all t > 0 is not in general possible for reasons that are fundamental to the fractal setting, but we are able to obtain single scale (t ∈ [1, 2]) results. The ran...

Lower bounds of Copson type for the transpose of matrices on weighted sequence spaces

Conditional Stein approximation for Itô and Skorohod integrals

We derive conditional Edgeworth-type expansions for Skorohod and Itô integrals with respect to Brownian motion, based on cumulant operators defined by the Malliavin calculus. As a consequence we obtain conditional Stein approximation bounds for multiple stochastic integrals and quadratic Brownian functionals.

Some inequalities involving lower bounds of operators on weighted sequence spaces by a matrix norm

Let A = (an;k)n;k1 and B = (bn;k)n;k1 be two non-negative ma-trices. Denote by Lv;p;q;B(A), the supremum of those L, satisfying the followinginequality:k Ax kv;B(q) L k x kv;B(p);where x 0 and x 2 lp(v;B) and also v = (vn)1n=1 is an increasing, non-negativesequence of real numbers. In this paper, we obtain a Hardy-type formula forLv;p;q;B(H), where H is the Hausdor matrix and 0 < q p 1. Also...