A NEW APPROACH TO NORM INEQUALITIESON WEIGHTED AND VARIABLE HARDY SPACES

摘要

We give new proofs of Hardy space estimates for fractional andsingular integral operators on weighted and variable exponent Hardyspaces. Our proofs consist of several interlocking ideas: finiteatomic decompositions in terms of L atoms, vector-valued inequalities for maximal and other operators, and Rubio deFrancia extrapolation. Many of these estimates are not new, but wegive new and substantially simpler proofs, which in turn significantlysimplifies the proofs of the Hardy spaces inequalities.