Entropy numbers of functions on [−1,1] with Jacobi weights

We study the entropy numbers of weighted Sobolev classes BWp,α,βr in Lq,α,βLq,α,β, where Lq,α,β,1≤q≤∞Lq,α,β,1≤q≤∞ denotes the weighted LqLq space on [−1,1][−1,1] with respect to weight wα,β(x):=(1−x)α(1+x)β,α,β>−1/2. Exact orders of the entropy numbers are obtained for all 1≤p,q≤∞1≤p,q≤∞ and α,β>−1/2α,β>−1/2.