Two-Weight Norm Inequalities for the Local Maximal Function

Weighted Norm Inequalities for the Local Sharp Maximal Function

Two weight norm inequalities for fractional one-sided maximal and integral operators

In this paper, we give a generalization of Fefferman-Stein inequality for the fractional one-sided maximal operator: Z +∞ −∞ M α (f)(x) w(x) dx ≤ Ap Z +∞ −∞ |f(x)|M αp(w)(x) dx, where 0 < α < 1 and 1 < p < 1/α. We also obtain a substitute of dual theorem and weighted norm inequalities for the one-sided fractional integral I α .

Two-Weight Orlicz Type Integral Inequalities for the Maximal Operator

p A v = u  , (1) holds for t = ) t ( = ) t (   , but not if 1 = p . Also for each   < p 1 there exists a pair p A ) v , u (  so that (1) fails in the special case t = ) t ( = ) t (   [3, p. 395]. In these exceptional cases we have a weak type inequality. An excellent reference is the book by J.Garcia-Cuerva and J.L.Rubio de Francia [3]. We refer the reader interested in the current stat...

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...

Maximal Inequalities for Associated Random Variables

In a celebrated work by Shao [13] several inequalities for negatively associated random variables were proved. In this paper we obtain some maximal inequalities for associated random variables. Also we establish a maximal inequality for demimartingales which generalizes and improves the result of Christofides [4].