Sobolev's inequality for Riesz potentials with variable exponent satisfying a log-Hölder condition at infinity
Sobolev's inequality for Riesz potentials with variable exponent satisfying a log-Hölder condition at infinity
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DOI：
10.1016/j.jmaa.2005.02.046
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发表时间：
2005-11
影响因子：
1.3
通讯作者：
Y. Mizuta;T. Shimomura
中科院分区：
文献类型：
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作者：
Y. Mizuta;T. Shimomura
本文研究了广义Lebesgue空间Lp（λ）中极大函数在无穷远处满足log-Hölder条件时的有界性，这个条件比Cruz-Uribe，Fiorenza和Neugebauer [D. Cruz-Uribe，A.张文，变L_p空间上的极大函数，中国科学院学报，2001。Sci.芬恩28（2003）223-238; 29（2004）247-249]。我们的结果推广了Diening [L. Diening，广义Lp（ε）空间上的极大函数，数学不等式。7（2004）245-254]和作者Futamura和Mizuta [T. Futamura，Y. Mizuta，Sobolev embeddings for Riesz potential space of variable exponent，preprint].作为极大函数有界性的一个应用，我们证明了变指数Riesz势的Sobolev不等式。
Our aim in this paper is to deal with the boundedness of maximal functions in generalized Lebesgue spaces Lp(⋅)when p(⋅) satisfies a log-Hölder condition at infinity that is weaker than that of Cruz-Uribe, Fiorenza and Neugebauer [D. Cruz-Uribe, A. Fiorenza, C.J. Neugebauer, The maximal function on variable Lpspaces, Ann. Acad. Sci. Fenn. Math. 28 (2003) 223–238; 29 (2004) 247–249]. Our result extends the recent work of Diening [L. Diening, Maximal functions on generalized Lp(⋅)spaces, Math. Inequal. Appl. 7 (2004) 245–254] and the authors Futamura and Mizuta [T. Futamura, Y. Mizuta, Sobolev embeddings for Riesz potential space of variable exponent, preprint]. As an application of the boundedness of maximal functions, we show Sobolev's inequality for Riesz potentials with variable exponent.