Off-diagonal estimates for commutators of bi-parameter singular integrals

Abstract

We study the boundedness of commutators of bi-parameter singular integrals between mixed spaces $$[b,T]:L^{p_1}{L}^{p_2}\to L^{q_1}{L}^{q_2}$$ in the off-diagonal situation $q_i,p_i\in (1,\infty )$ where we also allow $q_i\ne p_i.$ Boundedness is fully characterized for several arrangements of the integrability exponents with some open problems presented.

V1: 36 pages. V2: Improved presentation with typos removed, 32 pages

References in corpus (2)

• The L^p-to-L^q boundedness of commutators with applications to the Jacobian operator
• On the Hardy space theory of compensated compactness quantities