In this paper, we obtain an explicit formula of general solution for a class of the non-homoge- neous recurrence of variable coefficients with two indices.
Yu Chang-an College of Mathematics and Computer Science, Wuhan University, Wuhan 430072,China
Several theorems for atomic decompositions of Banach-space-valued martingales are proved. As their applications, the relationship among some martingale spaces such as H_α(X) and _ρ(?)_α in the case 0<α≤1 are studied. It is shown that there is a close connection between the results and the smoothness and convexity of the value spaces.
In martingale setting, it has been shown that Ap weights can be factorized in terms of A 1 weights. This factorization benefits many problems very much. In this paper, the new class of RH ∞ plays the same role for RH s , which makes the reverse Hlder inequalities hold with exponent s>1 , that the class A 1 does for A p class. Therefore, the Jones’ factorization theorem for A p weights was extended to include some information about the reverse Hlder classes. And it is the most convenient object in weight theory indeed.
