Entropy numbers of Sobolev embeddings of radial Besov spaces Original Research Article

Let RBp,qs(Rn) be the radial subspace of the Besov space Bp,qs(Rn). We prove the independence of the asymptotic behavior of the entropy numbersek(id : RBp0,q0s0(Rn)↦RBp1,q1s1(Rn))from the difference s0−s1 as long as the embedding itself RBp0,q0s0(Rn)↪RBp1,q1s1(Rn) is compact. In fact, we shall show thatek(id : RBp0,q0s0(Rn)↦RBp1,q1s1(Rn))∼k−n(1p0−1p1).This is in a certain contrast to earlier results on entropy numbers in the context of Besov spaces Bp,qs(Ω) on bounded domains Ω.