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Boundedness of Marcinkiewicz integral on Triebel-Lizorkin spaces
  • 期刊名称：Applied Mathematics-A Journal of Chinese Universit
  • 时间：2010.2.2
  • 页码：48-54
  • 分类：O174.2[理学—数学;理学—基础数学]
  • 作者机构：[1]浙江大学数学系,杭州310027, [2]浙江外国语学院数学系,杭州310012, [3]浙江理工大学数学科学系,杭州310018
  • 相关基金：国家自然科学基金资助项目（10931001 10871173）
  • 相关项目：调和分析及其应用
作者： Zhang, Chun-jie|Chen, Jie-cheng|
关键词： LORENTZ空间, 连续模, 权, Lorentz spaces, moduli of continuity, weight
中文摘要：

证明了在加权Lorentz空间上联系偏导数和偏连续模的Gagliardo-Nirenberg型乘积型不等式.我们的主要结果是下面的不等式和,其中0〈θ〈1,1/p=1-θ/p_0＋θ/p_1,1/s=1-θ/s_0＋θ/s_1,且指标p_i,s_i和权w满足一些特殊条件.同时给出了C和K具体估计.

英文摘要：

We prove multiplicative inequalities of Gagliardo-Nirenberg type that connect partial moduli of continuity and partial derivatives of functions with respect to a fixed variable in different weighted Lorentz norms.Our main results are the estimates and where 0θ1,1/p=1-θ/p_0＋θ/p_1,1/s=1-θ/s_0＋θ/s_1,with exponents p_i,s_i and weight w satisfying some special conditions.Furthermore,we give concrete estimates of Cand K.

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