WEIGHTED Lp BOUNDEDNESS FOR MULTILINEAR FRACTIONAL INTEGRAL ON PRODUCT SPACES

For 0 < α < mn and nonnegativeintegers n ≥ 2,m ≥ 1, the multilinear fractional integral is defined by Iα(m )(→f )(x) = ∫(Rn)m 1/ ︱→y |mn-α m ∏ i=1 fi(x-yi)d→y , where →y = (y1,y2,··· ,ym) and →f denotes the m-tuple (f1, f2,··· , fm). In this note, the one-weighted and two-weighted boundednesson Lp(Rn) space for multilinear fractional integral operator Iα(m )and the fractional multi-sublinear maximal operator Mα(m )are established re-spectively. The authors also obtain two-weighted weak type estimate for the...