Norm inequalities for some singular integral operators

Weighted norm inequalities for singular integral operators

Weighted Norm Inequalities for Maximally Modulated Singular Integral Operators

We present a framework that yields a variety of weighted and vector-valued estimates for maximally modulated Calderón-Zygmund singular (and maximal singular) integrals from a single a priori weak type unweighted estimate for the maximal modulations of such operators. We discuss two approaches, one based on the good-λ method of Coifman and Fefferman [CF] and an alternative method employing the s...

Some sharp inequalities for multilinear integral operators

In this paper, some sharp inequalities for certain multilinear operators related to the Littlewood-Paley operator and the Marcinkiewicz operator are obtained. As an application, we obtain the (L p , L q)-norm inequalities and Morrey spaces boundedness for the multilinear operators.

Inequalities for Norms of Some Integral Operators

Let (A(a)u)(x) := a 0 (1 − xt) −1 u(t) dt, 0 < a < 1. Properties of the operators A(a) as a → 1 are studied. It is proved that A := A(1) is a bounded, positive self-adjoint operator in H = L 2 [0, 1], ||A|| ≤ π, while A : C(0, 1) → C(0, 1) is unbounded.

Weighted norm inequalities for singular integral operators satisfying a variant of Hörmander’s condition

In this paper we establish weighted norm inequalities for singular integral operators with kernel satisfying a variant of the classical Hörmander’s condition.