加权Lorentz空间上的连续模和Gagliardo--Nirenberg型不等式

李宏亮, 徐罕

数学学报 ›› 2010, Vol. 53 ›› Issue (6) : 1225-1238.

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数学学报 ›› 2010, Vol. 53 ›› Issue (6) : 1225-1238. DOI: 10.12386/A2010sxxb0137
论文

加权Lorentz空间上的连续模和Gagliardo--Nirenberg型不等式

    李宏亮1,2, 徐罕3
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A Note on Inequalities of Gagliardo–Nirenberg Type and the Moduli of Continuity

    Hong Liang LI1,2, Han XU3
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文章历史 +

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,且指标pi,si 和权w满足一些特殊条件. 同时给出了C和K具体估计.  

Abstract

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 , with exponents pi, si and weight w satisfying some special conditions. Furthermore, we give concrete estimates of C and K.  

关键词

Lorentz空间 / 连续模 / 权

Key words

Lorentz spaces / moduli of continuity / weight

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李宏亮, 徐罕. 加权Lorentz空间上的连续模和Gagliardo--Nirenberg型不等式. 数学学报, 2010, 53(6): 1225-1238 https://doi.org/10.12386/A2010sxxb0137
Hong Liang LI, Han XU. A Note on Inequalities of Gagliardo–Nirenberg Type and the Moduli of Continuity. Acta Mathematica Sinica, Chinese Series, 2010, 53(6): 1225-1238 https://doi.org/10.12386/A2010sxxb0137

参考文献



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基金

国家自然科学基金资助项目(10931001,10871173)

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