Weighted norm inequalities for a general maximal operator

Maximal Operator and Weighted Norm Inequalities for Multilinear Singular Integrals

The analysis of multilinear singular integrals has much of its origins in several works by Coifman and Meyer in the 70’s; see for example [3]. More recently, in [4] and [5], an updated systematic treatment of multilinear singular integral operators of Calderón-Zygmund type was presented in light of some new developments. See also [6] and the references therein for a detailed description of prev...

Weighted Norm Inequalities for the Local Sharp Maximal Function

Some weighted operator geometric mean inequalities

In this paper, using the extended Holder- -McCarthy inequality, several inequalities involving the α-weighted geometric mean (0<α<1) of two positive operators are established. In particular, it is proved that if A,B,X,Y∈B(H) such that A and B are two positive invertible operators, then for all r ≥1, ‖X^* (A⋕_α B)Y‖^r≤‖〖(X〗^* AX)^r ‖^((1-α)/2) ‖〖(Y〗^* AY)^r ‖^((1-α)/2) ‖〖(X〗^* BX)^r ‖^(α/2) ‖〖(Y...

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) =...

Norm Comparison Inequalities for the Composite Operator

The purpose of this paper is to establish the Lipschitz norm and BMO norm inequalities for the composition of the homotopy operator T and the projection operator H applied to differential forms in R, n ≥ 2. The harmonic projection operator H, one of the key operators in the harmonic analysis, plays an important role in the Hodge decomposition theory of differential forms. In the meanwhile, the ...