On the Four Conjectures of G G Lorentz Type in L_ρ~2[-a,a]

关于L_ρ~2[-a,a]中G.G.Lorentz型的四个猜想(英文)

In the space C[-1,1],G G Lorentz proposed four conjectures on the properties of the polynomials of the best approximation in 1977,1978 and 1980.The present paper transplants the four conjectures in the space Lρ2[-a,a] and proves them being all right in only one theorem under the corresponding conditions,although each of the original conjectures is very difficulty.