Off-diagonal estimates for bi-commutators

Abstract

We study the bi-commutators $[T_1,[b,T_2]]$ of pointwise multiplication and Calderón-Zygmund operators, and characterize their $L^{p_1}{L}^{p_2}\to L^{q_1}{L}^{q_2}$ boundedness for several off-diagonal regimes of the mixed-norm integrability exponents $(p_1,p_2)\ne (q_1,q_2)$. The strategy is based on a bi-parameter version of the recent approximate weak factorization method.

arXiv comment46 pages

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Cited by in corpus (2)

• Lower bound of the parabolic Hilbert commutator
• Approximation in Hölder Spaces