Interpolation theorems for variable exponent Lebesgue spaces

When Hardy–Littlewood maximal operator is bounded on Lp(·)(Rn) space we prove [Lp(·)(Rn), BMO(Rn)]θ = Lq(·)(Rn) where q(·) = p(·)/(1 − θ) and [Lp(·)(Rn),H1(Rn)]θ = Lq(·)(Rn) where 1/q(·) = θ + (1− θ)/p(·). © 2009 Elsevier Inc. All rights reserved.