Multilinear Square Functions with Kernels of Dini’s Type

Abstract EN

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.