$L^p$ weighted inequalities for the dyadic square function

The Weighted Square Integral Inequalities for the First Derivative of the Function of a Real Variable

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

Weighted Norm Inequalities for the Local Sharp Maximal Function

Sharp Weighted Inequalities for the Vector–valued Maximal Function

We prove in this paper some sharp weighted inequalities for the vector–valued maximal function Mq of Fefferman and Stein defined by Mqf(x) = ( ∞ ∑ i=1 (Mfi(x)) q )1/q , where M is the Hardy–Littlewood maximal function. As a consequence we derive the main result establishing that in the range 1 < q < p < ∞ there exists a constant C such that ∫ Rn Mqf(x) p w(x)dx ≤ C ∫ Rn |f(x)|qM [ p q ]+1 w(x)d...

Some Inequalities for the Lp-Curvature Image

Lutwak introduced the notion of Lp-curvature image and proved an inequality for the volumes of convex body and its Lp-curvature image. In this paper, we first give an monotonic property of Lpcurvature image. Further, we establish two inequalities for the Lp-curvature image and its polar, respectively. Finally, an inequality for the volumes of Lp-projection body and Lp-curvature image is obtained.