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(⋅).