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In this paper, we determine the infimum and the supremum of the Diricht ∈ [0, T], where 1 ＜ p ＜∞, and the weights ρ are nonnegative and are subject toconditions ∫01 ρ(t)dt = M and maxt∈[0,T] p(t) = H. It is also explained for what weights p the infimum and the supremum will be attained.