Estimates of Marcinkiewicz Integrals with Bounded Homogeneous Kernels of Degree Zero期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Estimates of Marcinkiewicz Integrals with Bounded Homogeneous Kernels of Degree Zero

Authors:	Email author" target="_blank">Jaesung?Lee Email author Kyung Soo?Rim

Institution:	(1) Department of Mathematics, Sogang University, Seoul, 121-742, Korea;(2) UDIP Lab Corp., Bangwoo B/D 4FL 636-2 Shinsa Kangnam, 135-896 Seoul, Korea

Abstract:	Under the cancellation property and a certain Dini-type condition on kernels, we prove that Marcinkiewicz integrals with kernels which are homogeneous functions of degree zero, are bounded from $H^1 (\mathbb{R}^n)$ to $L^1 (\mathbb{R}^n)$ , from $L^\infty (\mathbb{R}^n)$ to $BMO (\mathbb{R}^n)$ , and from $L^p (\mathbb{R}^n)$ to $L^p (\mathbb{R}^n)$ for $1 < p < \infty$ .

Keywords:	Primary: 42B20 Secondary: 47B38
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