Abstract
AbstractWe find a minimal notion of non-degeneracy for bilinear singular integral operatorsTand identify testing conditions on the multiplying functionbthat characterize theLp×Lq→Lr,$1<p,q<\infty $1<p,q<∞and$r>\frac {1}{2},$r>12,boundedness of the bilinear commutator [b,T]1(f,g) =bT(f,g) −T(bf,g). Our arguments cover almost all arrangements of the integrability exponentsp,q,rwith a single open problem presented in the end. Additionally, the arguments extend to the multilinear setting.
Funder
Academy of Finland
Helsingin Yliopisto
University of Helsinki including Helsinki University Central Hospital
Publisher
Springer Science and Business Media LLC
Reference22 articles.
1. Airta, E., Hytönen, T., Li, K., Martikainen, H., Oikari, T.: Off-Diagonal Estimates for Bi-Commutators, Int. Math. Res. Not. (202109)
2. Airta, E., Li, K., Martikainen, H., Vuorinen, E.: Some new weighted estimates on product spaces. Indiana Univ. Math. J. 71, 37–63 (2022)
3. Alexander, B.: Weighted estimates for rough bilinear singular integrals via sparse domination. New York J. Math. 23 (2017)
4. Chaffee, L.: Characterizations of bounded mean oscillation through commutators of bilinear singular integral operators. Proc. R. Soc. Edinb. 146(6), 1159–1166 (2016)
5. Coifman, R., Lions, P.-L., Meyer, Y., Semmes, S.: Compensated compactness and Hardy spaces. J. Math. Pures Appl. 9, 247–286 (1993)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献