Multilinear Square Functions with Kernels of Dini's Type
Multilinear Square Functions with Kernels of Dini's Type
复制标题
具有 Dini 型核的多线性平方函数
DOI：
10.1155/2016/4876146
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发表时间：
2016-01-01
影响因子：
1.9
通讯作者：
Xue, Qingying
中科院分区：
文献类型：
--
作者：
Si, Zengyan;Xue, Qingying
设T是核满足Dini（1）条件的多线性平方函数，T* 是相应的多线性极大平方函数.在本文中，我们首先证明了T是从L-1 x…x L-1至L-1/m，L-无穷大。其次，我们得到了：如果每个P-i > 1，则T和T* 从L-P1（omega（1））x. x L-Pm（omega（m））到L-P（右箭头上的nu（omega）），并且如果P-i = 1，则T和T* 从L-P1（omega（1））x. x L-Pm（omega（m））到L-P，L-无穷大（右箭头上的nu（omega）），其中右箭头上的nu（omega）= Pi（m）（i=1）omega（p/pi）（i）。进一步，我们分别建立了T和T* 在加权Morrey型空间上的加权强型和加权弱型有界性.
Let T be a multilinear square function with a kernel satisfying Dini(1) condition and let T* be the corresponding multilinear maximal square function. In this paper, first, we showed that T is bounded from L-1 x ... x L-1 to L-1/m,L-infinity. Secondly, we obtained that if each P-i > 1, then T and T* are bounded from L-P1(omega(1)) x ... x L-Pm (omega(m)) to L-P(nu(omega) over right arrow) and if there is P-i = 1, then T and T* are bounded from L-P1(omega(1)) x ... x L-Pm (omega(m)) to L-P,L-infinity(nu(omega) over right arrow), where nu(omega) over right arrow = Pi(m)(i=1)omega(p/pi)(i). Furthermore, we established the weighted strong and weak type boundedness for T and T* on weighted Morrey type spaces, respectively.