Weighted and vector-valued inequalities for potential operators

Abstract

ABSTRACT.In this paper we develop some aspect of a general theory parallel to the Calderón-Zygmund theory for operator valued kernels, where the operators considered map functions defined on Rn into functions defined on Rn+1 = Rn x [0)OO).In particular, we apply the obtained results to get vector-valued inequalities for the Poisson integral and fractional integrals.Some weighted norm inequalities are also considered for fractional integrals.

A Characterization of Two Weight Norm Inequalities for Fractional and Poisson Integrals

“…For other work on weighted inequalities for these operators, see [2,4,6,7,9,10,11,15,17,20,21,22,23,27,30,32,35,36,39] and references given there. Before stating our two theorems, we establish some notation.…”

A new approach to norm inequalities on weighted and variable Hardy spaces

“…A similar inequality also holds for the fractional maximal operator, M α , 0 < α < n, and is due to Ruiz and Torrea [31]:…”