Off-diagonal estimates for bi-parameter commutators - Oikari, Tuomas (Annales Fennici Mathematici, 2022)
We study the boundedness of commutators of bi-parameter singular integrals between mixed spaces \([b,T]L^p_1L^p_2 → L^q_1L^q_2\) in the off-diagonal situation \(q_i,p_i(1,∞)\) where we allow \(q_i ot= p_i\). 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.