On the smoothness of slowly varying functions

Abstract

In this paper we consider the question of smoothness of slowly varying functions satisfying the modern definition that, in the last two decades, gained prevalence in the applications concerning function spaces and interpolation. We show, that every slowly varying function of this type is equivalent to a slowly varying function that has continuous classical derivatives of all orders.

arXiv admin note: text overlap with arXiv:2006.14455

References in corpus (2)

• Reduction principle for Gaussian $K$-inequality
• On Bilinear Hardy Inequality and Corresponding Geometric Mean Inequality

Cited by in corpus (1)

• Optimal function spaces in weighted Sobolev embeddings with $\alpha$-homogeneous weights