Restricted testing for the Hardy-Littlewood maximal function

Abstract

We answer a special case of a question of T. Hytonen regarding the two weight norm inequality for the maximal function M in the affirmative, namely that there is a constant D > 1, depending only on dimension n, such that the two weight norm inequality for M holds if and only if the A_2 condition holds, and the testing condition holds for all doubling cubes.

33 pages

References in corpus (5)

• Two weight estimate for the Hilbert transform and corona decomposition for non-doubling measures
• Two Weight Inequalities for Riesz Transforms: Uniformly Full Dimension Weights
• Two weight norm inequalities for the $g$ function
• Two Weight Inequalities for the Cauchy Transform from $\mathbb{R}$ to ${\mathbb{C}}_{+}$
• Energy conditions and twisted localizations of operators

Cited by in corpus (1)

• Two Weight Inequalities for Positive Operators: Doubling Cubes