Resumen de Estimates for continuity envelopes and approximation numbers of Bessel potentials

Mikhail L. Goldman, Dorothee Haroske

• In this paper we study spaces of Bessel potentials in n-dimensional Euclidean spaces. They are constructed on the basis of a rearrangement-invariant space (RIS) by using convolutions with Bessel.

  MacDonald kernels. Specifically, the treatment covers spaces of classical Bessel potentials. We establish two-sided estimates for the corresponding modulus of smoothness of order k �¸ N, �Ök ( f ; t), and determine their continuity envelope functions. This result is then applied to estimate the approximation numbers of some embeddings.