Abstract
We give a necessary and sufficient condition for the two weight Lp-estimates for paraproducts in non-homogeneous settings, 1<p<∞. We are mainly interested in the case p≠2, since the case p=2 is a well-known and easy corollary of the Carleson embedding theorem. The necessary and sufficient condition is given in terms of testing conditions of Sawyer type: for p≤2 only one (“direct”) testing condition is required, but for p>2 both “direct” and “adjoint” testing conditions are needed. An interesting feature is that the “adjoint” testing condition is that it is a testing condition not for the adjoint of the paraproduct, but for some auxiliary operator.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
