Singular and fractional integral operators on Campanato spaces with variable growth conditions
Singular and fractional integral operators on Campanato spaces with variable growth conditions
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DOI：
10.1007/s13163-009-0022-y
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发表时间：
2010-07
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影响因子：
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通讯作者：
E. Nakai
中科院分区：
文献类型：
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作者：
E. Nakai
设X是Coifman和韦斯意义下的齐型空间。本文证明了奇异积分算子和分数次积分算子在X上的Campanato空间上的有界性。函数空间包含变指数的广义Lipschitz空间作为特例。此外，利用函数空间，我们还可以处理X中一个子集上局部为Lp-函数，另一个子集上局部为BMO-函数，另一个子集上局部为Lipα-函数的函数.我们的研究结果甚至对于非线性系统也是新的。
LetXbe a space of homogeneous type in the sense of Coifman and Weiss. In this paper, we prove boundedness of singular and fractional integral operators on Campanato spaces overXwith variable growth conditions. The function spaces contain generalized Lipschitz spaces with variable exponent as special cases. Moreover, by using the function spaces, we can deal with functions which areLp-functions locally on one subset inX, BMO-functions locally on one another subset and Lipα-functions locally on the other one. Our results are new even for ℝncase.