Abstract
LetTbe a multilinear square function with a kernel satisfying Dini(1) condition and letT⁎be the corresponding multilinear maximal square function. In this paper, first, we showed thatTis bounded fromL1×⋯×L1toL1/m,∞.Secondly, we obtained that if eachpi>1, thenTandT⁎are bounded fromLp1(ω1)×⋯×Lpm(ωm)toLp(νω→)and if there ispi=1, thenTandT⁎are bounded fromLp1(ω1)×⋯×Lpm(ωm)toLp,∞(νω→), whereνω→=∏i=1mωip/pi.Furthermore, we established the weighted strong and weak type boundedness forTandT⁎on weighted Morrey type spaces, respectively.
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