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Boundedness of Marcinkiewicz integrals with rough kernels on Musielak-Orlicz Hardy spaces
Bo Li1, Minfeng Liao1, Baode Li1
1College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046 P.R. China.
Abstract:
Let [Formula: see text] satisfy that [Formula: see text], for any given [Formula: see text], is an Orlicz function and [Formula: see text] is a Muckenhoupt [Formula: see text] weight uniformly in [Formula: see text]. The Musielak-Orlicz Hardy space [Formula: see text] is defined to be the set of all tempered distributions such that their grand maximal functions belong to the Musielak-Orlicz space [Formula: see text]. In this paper, the authors establish the boundedness of Marcinkiewicz integral [Formula: see text] from [Formula: see text] to [Formula: see text] under weaker smoothness conditions assumed on Ω. This result is also new even when [Formula: see text] for all [Formula: see text], where ϕ is an Orlicz function.
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