Non-homogeneous T1 theorem for bi-parameter singular integrals

Abstract

We prove a non-homogeneous T1 theorem for certain bi-parameter singular integral operators. Moreover, we discuss the related non-homogeneous Journe's lemma and product BMO theory.

v2: Substantial revision with a better version of the main theorem (diagonal BMO assumptions weakened). 45 pages

References in corpus (4)

• The Hardy Space $H^1$ on Non-homogeneous Metric Spaces
• Variations on the Theme of Journe's Lemma
• The vector-valued non-homogeneous Tb theorem
• A T(1) theorem on product spaces

Cited by in corpus (2)

• Some obstacles in characterising the boundedness of bi-parameter singular integrals
• A T(b) Theorem on Product Spaces