The Riesz potential as a multilinear operator into general BMO_{beta} sp aces

HUGO AIMAR; SILVIA HARTZSTEIN; BIBIANA IAFFEI; BEATRIZ VIVIANI

JOURNAL OF MATHEMATICAL SCIENCES

Springer

Lugar: New York; Año: 2010

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 Lp_1 x...x Lp_k for the range of $1/p_i = 1/p_1 +...+1/p_k  - alpha/n leq 0$. We show that the target space is an adequate space BMO_{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 = R^n (n is a natural number), we can extend the result to beta > 0 taking in account that BMO_{beta} is a space of classes modulii polynomials of order lower than or equal to [beta].