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A note on commutators of Hardy operators
Authors:Fayou Zhao
Institution:Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China
Abstract:Fu and Lu et al. 7 showed that the commutator $\mathcal {H}_{\beta ,b}$ generated by the fractional Hardy operator and a locally integrable function b is bounded on the homogenous Herz spaces if and only if b is a central bounded mean oscillation function. We show that their result is optimal by giving a counterexample.
Keywords:Central BMO spaces  n‐dimensional Hardy operators  commutators  optimal  msc (2010) Primary: 47G10  47H60  Secondary: 26D15  47A63  47A30
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