Characterization of Higher-Order Sobolev Spaces on the Sphere via Generalized Averaging of Function
Functional Analysis
2025-06-24 v1
Abstract
We present a new characterization of higher-order Sobolev spaces on the sphere. Building on the approach of Barcel\'o et al. (2020), we refine the square function they introduced for this purpose. In particular, we provide a detailed analysis of the weight function and the averaging range in its definition. Our results demonstrate that averaging can be performed using a weight function from a broad class, and that the averaging domain can be restricted to a local coordinate patch on the sphere.
Cite
@article{arxiv.2506.17736,
title = {Characterization of Higher-Order Sobolev Spaces on the Sphere via Generalized Averaging of Function},
author = {Ikhsan Maulidi and Hiroshi Ohtsuka},
journal= {arXiv preprint arXiv:2506.17736},
year = {2025}
}