Algorithmic complexity of NP-hard sets

We strengthen results of Dekhtyar. The paper contains a new result on structure of $NP$-hard sets. We prove that the kolmogorov recognition complexity (with polynomially bound time) of $NP$-hard sets (with polynomial Turing reducibility) can't be less than $O(\lg\lg n)$ if $NP\neq P$ for initial segment with $n$ elements.