info:eu-repo/semantics/article
The Riesz potential as a multilinear operator into general BMOβ spaces
Fecha
2011-03Registro en:
Aimar, Hugo Alejandro; Hartzstein, Silvia Inés; Iaffei, Bibiana Raquel; Viviani, Beatriz Eleonora; The Riesz potential as a multilinear operator into general BMOβ spaces; Springer Science; Journal Of Mathematical Sciences; 173; 6; 3-2011; 643-655
1072-3374
CONICET Digital
CONICET
Autor
Aimar, Hugo Alejandro
Hartzstein, Silvia Inés
Iaffei, Bibiana Raquel
Viviani, Beatriz Eleonora
Resumen
Given α > 0 and a space of homogeneous type X, n-normal, with n ℝ+, we consider an extension of the standard multilinear fractional integral on Lp1 × ... × Lpk for the range of 1/pi = 1/p1...+1/pk -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 = ℝn (n ∈ N), 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]. Bibliography: 15 titles.