Some results of S. N. Bernstein about polynomials of least deviation from zero in some weighted spaces L _p are generalized to entire functions of exponential type. Suppose that a function ρm belongs to the Cartwright class, is of type m, is positive on the real axis, and let σ ≥ m. Earlier, the authors constructed functions least deviating from zero among entire functions of type σ in the uniform and integral metrics on R with the weights ω = 1/ρm and ω =