科研之友
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摘要
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.
