Projects per year
Abstract
We prove the mixednorm LpLqboundedness of a general class of singular integral operators having a multiparameter singularity and acting on vectorvalued (UMD Banach latticevalued) functions. Moreover, families of such operators with uniform assumptions are shown to be not only uniformly bounded but Rbounded, a genuinely stronger property that is often needed in applications. Previous results of this nature only dealt with convolutiontype or slightly more general paraproductfree singular integrals. In contrast, our analysis specifically targets the array of different partial paraproducts that arise in the multiparameter setting by interpreting them as paraproductvalued oneparameter operators. This new pointofview provides a conceptual simplification over the existing representation results for multiparameter operators, which is a key to the proof of the boundedness of these operators.
Original language  English 

Journal  Proceedings of the London Mathematical Society 
Volume  119 
Issue number  6 
Pages (fromto)  15601597 
Number of pages  38 
ISSN  00246115 
DOIs  
Publication status  Published  Dec 2019 
MoE publication type  A1 Journal articlerefereed 
Fields of Science
 111 Mathematics
 42B20 (primary)
 SINGULARINTEGRALS
 DYADIC SHIFTS
 CALDERON
 REPRESENTATION
 INEQUALITIES
Projects
 1 Finished

Geometric and dyadic harmonic analysis: general measures and rectifiability
Martikainen, H. & Airta, E.
01/09/2016 → 31/08/2021
Project: Research project