The Riesz potential as Multilinear operator into General BMO spaces

AIMAR, H.; HARTZSTEIN, S.; IAFFEI, B; VIVIANI, B.

JOURNAL OF MATHEMATICAL SCIENCES

Springer Science

Año: 2011 vol. 173 p. 643 - 655

1072-3374

Given  alpha >0  and a space of homogeneous type X, n-normal, with n in R+,  we consider an extension of the standard multilinear fractional integral on Lp1 x       x Lpk    for the range of 1/p = 1/p1      +      +1/pk    - alpha/n  < = 0. We show that the target space is an adequate  Lipschitz integral space of order beta defined through mean oscillations. For general spaces of homogeneous type this is a Banach space of classes of functions modulii constants and the range of Beta  is [0, 1). However, if X = Rn  (n in N), we can extend the result to Beta > 0 taking in account that integral Lipschitz space is a space of classes modulii polynomials of order lower than or equal to [beta].