Cauchy-Szegö operator, quaternionic Siegel upper half space, commutator, weighted Morrey space

2020/06/17 by Fu, Zunwei, Gong, Ruming, Pozzi, Elodie +1
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2006.10546

Abstract

In the setting of quaternionic Heisenberg group \mathscr H^n-1, we characterize the boundedness and compactness of commutator [b,\mathcal C] for the Cauchy--Szegö operator \mathcal C on the weighted Morrey space L_w^{p, κ}(\mathscr H^n-1) with p∈(1, ∞), κ∈(0, 1) and w∈ A_p(\mathscr H^n-1). More precisely, we prove that [b,\mathcal C] is bounded on L_w^{p, κ}(\mathscr H^n-1) if and only if b∈ \rm BMO(\mathscr H^n-1). And [b,\mathcal C] is compact on L_w^{p, κ}(\mathscr H^n-1) if and only if b∈ \rm VMO(\mathscr H^n-1).

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