Commutators of Hilbert transforms along parabolic and monomial curves are bounded when the symbol lies in a curve-adapted BMO space, and a new testing BMO space gives a partial converse.
Boundedness results for commutators with BMO functions via weighted estimates: a comprehensive approach
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abstract
We present a unified method to obtain weighted estimates of linear and multilinear commutators with BMO functions, that is amenable to a plethora of operators and functional settings. Our approach elaborates on a commonly used Cauchy integral trick, recovering many known results but yielding also numerous new ones.
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Commutators of Hilbert transforms along monomial curves
Commutators of Hilbert transforms along parabolic and monomial curves are bounded when the symbol lies in a curve-adapted BMO space, and a new testing BMO space gives a partial converse.