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Necessary and sufficient conditions for boundedness of commutators associated with Calderón-Zygmund operators on slice spaces. (English) Zbl 1497.42047

In this paper, the authors established new versions of the Feferman-Stein inequality over the slice space and they further reobtained the boundedness of the Calderón-Zygmund operators with the standard kernel via a direct way rather than via the extrapolation on slice spaces. Moreover, they gave two necessary and sufficient conditions for the boundedness of the commutator \([b, T\Omega]\) generated by the locally integrable function \(b\) and the Calderón-Zygmund operator with the rough kernel \(T\Omega\) on slice spaces.

MSC:

42B35 Function spaces arising in harmonic analysis
30H35 BMO-spaces
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
26D10 Inequalities involving derivatives and differential and integral operators
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