Abstract
We prove the boundedness of commutators of high-dimensional Hausdorff operators <svg style="vertical-align:-4.37273pt;width:30.612499px;" id="M1" height="15.775" version="1.1" viewBox="0 0 30.612499 15.775" width="30.612499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.775)"> <g transform="translate(72,-59.38)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0">𝐻</tspan> </text> <text transform="matrix(1,0,0,-1,-61.03,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0">Φ</tspan> <tspan style="font-size: 8.75px; " x="6.6777759" y="0">,</tspan> <tspan style="font-size: 8.75px; " x="8.8657761" y="0">𝑏</tspan> </text> </g> </g> </svg> on Lebesgue space with central BMO function or Lipschitz function. Furthermore, the boundedness on Herz spaces and Morrey-Herz spaces is also obtained.
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