Weighted Rearrangement Inequalities for Local Sharp Maximal Functions

Complete Convergence and Some Maximal Inequalities for Weighted Sums of Random Variables

Let  be a sequence of arbitrary random variables with  and , for every  and  be an array of real numbers. We will obtain two maximal inequalities for partial sums and weighted sums of random variables and also, we will prove complete convergence for weighted sums , under some conditions on  and sequence .

Weighted Norm Inequalities for the Local Sharp Maximal Function

Sharp Weighted Bounds for Fractional Integral Operators

The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp bounds are obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities are obtained. Some of the techniques used include a sharp off-diagonal...

Sharp maximal and weighted estimates for multilinear iterated commutators of multilinear integrals with generalized kernels

In this paper, the authors establish the sharp maximal estimates for the multilinear iterated commutators generated by [Formula: see text] functions and multilinear singular integral operators with generalized kernels. As applications, the boundedness of this kind of multilinear iterated commutators on the product of weighted Lebesgue spaces and the product of variable exponent Lebesgue spaces ...

Sharp weighted norm inequalities for Littlewood–Paley operators and singular integrals

We prove sharp Lp(w) norm inequalities for the intrinsic square function (introduced recently by M. Wilson) in terms of the Ap characteristic of w for all 1 < p <∞. This implies the same sharp inequalities for the classical Lusin area integral S(f ), the Littlewood–Paley g-function, and their continuous analogs Sψ and gψ . Also, as a corollary, we obtain sharp weighted inequalities for any conv...