On some sharp weighted norm inequalities

On some sharp weighted norm inequalities

Given a weight , we consider the space ML which coincides with L p when ∈ Ap . Sharp weighted norm inequalities on ML for the Calderón–Zygmund and Littlewood–Paley operators are obtained in terms of the Ap characteristic of for any 1<p<∞. © 2005 Elsevier Inc. All rights reserved.

Weighted Norm Inequalities for the Local Sharp Maximal Function

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...

On Some Weighted Norm Inequalities for Littlewood–paley Operators

It is shown that the Lw,1< p<∞, operator norms of Littlewood–Paley operators are bounded by a multiple of ‖w‖ Ap , where γp = max{1, p/2} 1 p−1 . This improves previously known bounds for all p > 2. As a corollary, a new estimate in terms of ‖w‖Ap is obtained for the class of Calderón–Zygmund singular integrals commuting with dilations.

Weighted Norm Inequalities

Introduction In the rst part of the paper we study integral operators of the form (1) Kf(x) = v(x) x Z 0 k(x; y)u(y)f(y) dy; x > 0; where the real weight functions v(t) and u(t) are locally integrable and the kernel k(x; y) 0 satisses the following condition: there exists a constant D 1 such that Standard examples of a kernel k(x; y) 0 satisfying (2) are (i) k(x; y) = (x ? y) , 0 (ii) k(x; y) =...