Real interpolation of weighted tent spaces

Let p is an element of(0, infinity) and w is an element of A(infinity)(R-n) be a Muckenhoupt weight. In this article, the authors study the real interpolation of the weighted tent space T-w(p)(R-+(n+1)). For all w is an element of A(infinity)(R-n), theta is an element of(0, 1), 0 < p(0) < p(1) < infinity and q is an element of(0, infinity], the authors show that (T-w(p0) (R-+(n+1)), T-w(p1) (R-+(n+1)))(theta, q) = T-w(p, q) (R-+(n+1)), where 1/p = 1-theta/p(0) + theta/p(1) and T-w(p, q) (R-+(n+1)) denotes the weighted Lorentz-tent space, which is introduced in this article. As an application, the authors prove a real interpolation result on the weighted Hardy spaces Hp w(Rn) for all p is an element of(0, 1] and w is an element of A(infinity)(R-n), which, when w equivalent to 1, seals a gap existing in the original proof of a corresponding result of Fefferman et al.