Geodesic
Off-diagonal estimates for bi-parameter commutators
Tuomas Oikari1
1University of Jyväskylä, Department of Mathematics and Statistics
Annales Fennici Mathematici, Tome 48 (2023) no. 1, pp. 81-112

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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.
DOI : 10.54330/afm.125812
Keywords: Calderón-Zygmund operators, singular integrals, multi-parameter analysis, commutators

Tuomas Oikari  1

1 University of Jyväskylä, Department of Mathematics and Statistics 
Tuomas Oikari. Off-diagonal estimates for bi-parameter commutators. Annales Fennici Mathematici, Tome 48 (2023) no. 1, pp. 81-112. doi: 10.54330/afm.125812
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