An explicit formula for the quaternionic Cauchy-Szegő kernel is derived and used to prove Calderón-Zygmund kernel estimates, a pointwise kernel lower bound, and BMO/VMO commutator characterizations on the quaternionic Heisenberg group.
A revisit on the compactness of commutators
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abstract
A new characterization of CMO(R^n) is established by the local mean oscillation. Some characterizations of iterated compact commutators on weighted Lebesgue spaces are given, which are new even in the unweighted setting for the first order commutators.
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2019 1verdicts
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An explicit formula of Cauchy--Szeg\"{o} kernel for quaternionic Siegel upper half space and applications
An explicit formula for the quaternionic Cauchy-Szegő kernel is derived and used to prove Calderón-Zygmund kernel estimates, a pointwise kernel lower bound, and BMO/VMO commutator characterizations on the quaternionic Heisenberg group.