Two weight norm inequalities for the $g$ function

Two-weight Norm Inequalities for the Cesàro Means of Generalized Hermite Expansions

We prove two-weight norm inequalities for Cesàro means of generalized Hermite polynomial series and for the supremum of these means. A result about weak boundedness and an almost everywhere convergence result are also obtained.

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 .

The concentration function problem for $G$-spaces

‎In this note‎, ‎we consider the concentration function problem for a continuous action of a locally compact group $G$ on a locally compact Hausdorff space $X$‎. ‎We prove a necessary and sufficient condition for the concentration functions of a‎ ‎spread-out irreducible probability measure $mu$ on $G$ to converge to zero.

Conductor Inequalities and Criteria for Sobolev-lorentz Two-weight Inequalities

In this paper we present integral conductor inequalities connecting the Lorentz p, q-(quasi)norm of a gradient of a function to a one-dimensional integral of the p, q-capacitance of the conductor between two level surfaces of the same function. These inequalities generalize an inequality obtained by the second author in the case of the Sobolev norm. Such conductor inequalities lead to necessary...