Off-diagonal estimates for bi-parameter commutators

Authors

  • Tuomas Oikari University of Jyväskylä, Department of Mathematics and Statistics

Keywords:

Calderón-Zygmund operators, singular integrals, multi-parameter analysis, commutators

Abstract

We study the boundedness of commutators of bi-parameter singular integrals between mixed spaces
\([b,T]\colon L^{p_1}L^{p_2} \to L^{q_1}L^{q_2}\)
in the off-diagonal situation \(q_i,p_i\in(1,\infty)\) where we allow \(q_i\not= p_i\). Boundedness is fully characterized in terms of oscillatory testing conditions on the function \(b\) for a total seven out of the nine possible arrangements of the integrability exponents.
Section
Articles

Published

2022-12-31

How to Cite

Oikari, T. (2022). Off-diagonal estimates for bi-parameter commutators. Annales Fennici Mathematici, 48(1), 81–112. https://doi.org/10.54330/afm.125812