Multilinear Square Functions with Kernels of Dini's Type. (7th March 2016)

• Record Type: Journal Article
• Authors: Si, Zengyan; Xue, Qingying
• Other Names: Torres Rodolfo H. Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2016(2016)
• Publication Date: 2016-03-07
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2016/4876146
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : 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 × ⋯ × L 1 to L 1 / m, ∞ . Secondly, we obtained that if each p i > 1, then T and T ⁎ are bounded from L p 1 ( ω 1 ) × ⋯ × L p m ( ω m ) to L p ( ν ω → ) and if there is p i = 1, then T and T ⁎ are bounded from L p 1 ( ω 1 ) × ⋯ × L p m ( ω m ) to L p, ∞ ( ν ω → ), where ν ω → = ∏ i = 1 m ω i p / p i . Furthermore, we established the weighted strong and weak type boundedness for T and T ⁎ on weighted Morrey type spaces, respectively.