A Weighted Variant of Riemann-Liouville Fractional Integrals on Rn
A Weighted Variant of Riemann-Liouville Fractional Integrals on Rn
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DOI：
10.1155/2012/780132
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发表时间：
2012-01-01
影响因子：
--
通讯作者：
Yuan, Wen
中科院分区：
文献类型：
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作者：
Fu, Zun Wei;Lu, Shan Zhen;Yuan, Wen
在Rn上引入了Riemann-Liouville分数次积分的一类加权变式，并得到了它在中心Morrey空间和中心BMO空间上的精确界.此外，我们还建立了加权哈代算子（符号在中心BMO空间）的算子在中心Morrey空间上有界的权函数的充要条件.这些结果被进一步用来证明Weyl和塞萨罗的一些不等式的精确估计.
We introduce certain type of weighted variant of Riemann-Liouville fractional integral on R-n and obtain its sharp bounds on the central Morrey and lambda-central BMO spaces. Moreover, we establish a sufficient and necessary condition of the weight functions so that commutators of weighted Hardy operators (with symbols in lambda-central BMO space) are bounded on the central Morrey spaces. These results are further used to prove sharp estimates of some inequalities due to Weyl and Cesaro.