Two weight norm inequalities for the $g$ function

Michael T. Lacey, Kangwei Li

Type: Article

Publication Date: 2014-01-01

Citations: 11

DOI: https://doi.org/10.4310/mrl.2014.v21.n3.a9

Abstract

Given two weights σ, w on R n , the classical g-function satisfies the norm inequality g(fσ) L 2 (w)f L 2 (σ) if and only if the two weight Muckenhoupt A 2 condition holds, and a family of testing conditions holds, namelyuniformly over all cubes I ⊂ R n , and Q(I) is the Carleson box over I.A corresponding characterization for the intrinsic square function of Wilson also holds.

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Mathematical Research Letters - View - PDF
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