Abstract
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, ωk(f;t), and determine their continuity envelope functions. This result is then applied to estimate the approximation numbers of some embeddings.
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