Estimates for Littlewood–Paley operators in BMO(Rn)☆
Estimates for Littlewood–Paley operators in BMO(Rn)☆
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DOI：
10.1016/j.jmaa.2008.05.039
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发表时间：
2008-10
影响因子：
1.3
通讯作者：
Y. Meng;Dachun Yang
中科院分区：
文献类型：
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作者：
Y. Meng;Dachun Yang
设g（f）是Rn上f的Littlewood-Paley g-函数。本文证明了：若f∈BMO（Rn）（有界平均振动函数空间），则g（f）要么处处无穷，要么几乎处处有限，且在后一种情况下，[g（f）] 2从BMO（Rn）到BLO（Rn）（有界下振动函数空间）是有界的，BLO（Rn）是BMO（Rn）的一个真子空间.此外，对Lusin面积函数和Littlewood-Paley gλ* 函数也建立了类似的结果.
Let g(f) be the Littlewood–Paley g-function of f on Rn. In this paper, the authors prove that if f∈BMO(Rn) (the space of functions with bounded mean oscillation), then g(f) is either infinite everywhere or finite almost everywhere, and in the latter case, [g(f)]2is bounded from BMO(Rn) into BLO(Rn) (the space of functions with bounded lower oscillation), which is a proper subspace of BMO(Rn). Moreover, the authors also establish similar results for the Lusin-area function and the Littlewood–Paley gλ*-function.