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In this paper, for0  &lt;  γ  &lt;  1{0&lt;\gamma&lt;1}    andb  ∈    I  γ   ⁢   (  BMO  ){b\in I_{\gamma}(\mathrm{BMO})}   , the authors give theL  2   ⁢   (   ℝ  n   ){L^{2}({\mathbb{R}}^{n})}    boundedness ofμ   γ  ;  b{\mu_{\gamma;b}}   , the commutator of a fractional differential type Marcinkiewicz integral with rough variable kernel, which is an extension of some known results.

georgian mathematical journal

L  2      L^{2}    boundedness for commutators of fractional differential type Marcinkiewicz integral with rough variable kernel and BMO Sobolev spaces