Interpolation Between Hp(.)(Rn) and L∞(Rn): Real Method

Let p(.) : Rn. (0,8) be a variable exponent function satisfying the globally log-Holder continuous condition. In this article, the authors first obtain a decomposition for any distribution of the variable weak Hardy space into " good" and " bad" parts and then prove the following real interpolation theorem between the variable Hardy space H p(.)(Rn) and the space L 8 (Rn): (H p(.)(Rn), L 8 (Rn)).,8 = WHp(.)/(1-.)(Rn), where.. (0, 1), and WHp(.)/(1-.)(Rn) denotes the variable weak Hardy space. As an application, the variable weak Hardy space WHp(.)(Rn) with p-:= ess inf x. Rn p(x). (1,8) is proved to coincide with the variable Lebesgue space WLX is an element of Rnp(.)(R-n).