Abstract
In this paper, we study the boundedness of the commutators ofparametric Marcinkiewicz integral operator with smooth kernel on generalized Orlicz-Morrey spaces
Highlights
Suppose that Sn 1 is the unit sphere in Rn (n 2) equipped with the normalized Lebesgue measure d = d (x0)
Let b be a locally integrable function on Rn; the commutator generated by the parametric Marcinkiewicz integral and b is de...ned by
Boundedness of commutators of classical operators of harmonic analysis on generalized Orlicz-Morrey spaces were recently studied in various papers, see for example [3, 8, 9]
Summary
Let b be a locally integrable function on Rn; the commutator generated by the parametric Marcinkiewicz integral and b is de...ned by Parametric Marcinkiewicz integrals, generalized Orlicz-Morrey spaces, commutator, BMO. In words of [10], our generalized Orlicz-Morrey space is the third kind and the ones in [14] and [15] are the ...rst kind and the second kind, respectively. Boundedness of commutators of classical operators of harmonic analysis on generalized Orlicz-Morrey spaces were recently studied in various papers, see for example [3, 8, 9].
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