On the boundedness of the Marcinkiewicz operator on multipliers spaces
نویسنده
چکیده
Let h(y) be a bounded radial function and Ω (y) an H function on the unit sphere satisfying the cancelation condition. Then the Marcinkiewicz integral operator μΩ related to the Littlewood-Paley g−function is defined by
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ar X iv : m at h / 05 05 57 4 v 1 [ m at h . FA ] 2 6 M ay 2 00 5 On the boundedness the Marcinkiewicz operator on multipliers space By Sadek Gala
Let h(y) be a bounded radial function and Ω (y ′) an H 1 function on the unit sphere satisfying the cancelation condition. Then the Marcinkiewicz integral operator µ Ω related to the Littlewood-Paley g−function is defined by µ Ω (f)(x) = ∞ 0 |F t (x)| 2 dt t 3 1 2 , (1) where F t (x) = |x−y|≤t Ω (x − y) |x − y| d−1 h (|x − y|) f (y)dy (2) and h(y) ∈ L ∞ (R +). In this paper, we prove that the o...
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تاریخ انتشار 2008