The Riesz potential as a multilinear operator into general BMOβ spaces

AIMAR, HUGO; HARTZSTEIN, SILVIA; IAFFEI, BIBIANA; VIVIANI, BEATRIZ

JOURNAL OF MATHEMATICAL SCIENCES

Springer

Lugar: New York; Año: 2011 vol. 173 p. 643 - 655

1072-3374

Given α > 0 and a space of homogeneous type X, n-normal, with nR+, we consider an extension of the standard multilinear fractional integral on L p1 ×⋯× L pk for the range of 1/p i = 1/p 1⋯+1/p k −α/n ≤ 0. We show that the target space is an adequate space BMOβ 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 β is [0, 1). However, if                              X=RnnN , we can extend the result to β > 0 taking in account that BMOβ is a space of classes modulii polynomials of order lower than or equal to [β].