Projects per year
Abstract
We complete our theory of weighted
Lp (w(1)) x Lq (w(2)) > Lr (w(1)(r/p) w(2)(r/q))
estimates for bilinear biparameter CalderonZygmund operators under the assumption that w(1) is an element of A(p) and w(2 )is an element of A(q) are biparameter weights. This is done by lifting a previous restriction on the class of singular integrals by extending a classical result of Muckenhoupt and Wheeden regarding weighted BMO spaces to the product BMO setting. We use this extension of the MuckenhouptWheeden result also to generalise some twoweight commutator estimates from biparameter to multiparameter. This gives a fully satisfactory Bloomtype upper estimate for [T1, [T2, ...[b,Tk]]], where each Ti can be a completely general multiparameter CalderonZygmund operator.
Lp (w(1)) x Lq (w(2)) > Lr (w(1)(r/p) w(2)(r/q))
estimates for bilinear biparameter CalderonZygmund operators under the assumption that w(1) is an element of A(p) and w(2 )is an element of A(q) are biparameter weights. This is done by lifting a previous restriction on the class of singular integrals by extending a classical result of Muckenhoupt and Wheeden regarding weighted BMO spaces to the product BMO setting. We use this extension of the MuckenhouptWheeden result also to generalise some twoweight commutator estimates from biparameter to multiparameter. This gives a fully satisfactory Bloomtype upper estimate for [T1, [T2, ...[b,Tk]]], where each Ti can be a completely general multiparameter CalderonZygmund operator.
Original language  English 

Journal  Indiana University Mathematics Journal 
Volume  71 
Issue number  1 
Pages (fromto)  3763 
Number of pages  27 
ISSN  00222518 
DOIs  
Publication status  Published  2022 
MoE publication type  A1 Journal articlerefereed 
Fields of Science
 111 Mathematics
 Bilinear analysis
 biparameter analysis
 model operators
 weighted estimates
 SINGULARINTEGRALS
 EXTRAPOLATION
 REPRESENTATION
 INEQUALITIES
 OPERATORS
 BMO
Projects
 2 Finished

Singular integrals and the geometry of measures
Martikainen, H. & Oikari, T.
Valtion perusrahoitus/hankkeet
01/01/2018 → 31/12/2020
Project: University of Helsinki ThreeYear Research Project

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