Estimates for continuity envelopes and approximation numbers of Bessel potentials

Autores: Mikhail L. Goldman, Dorothee Haroske
Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 172, Nº 1, 2013, págs. 58-85
Idioma: inglés
DOI: 10.1016/j.jat.2013.04.005
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Resumen
- 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.