An Atomic Representation for Bicomplex Hardy Classes
Complex Variables
2025-10-07 v5 Analysis of PDEs
Classical Analysis and ODEs
Functional Analysis
Abstract
We develop representations for bicomplex-valued functions in Hardy classes that generalize the complex holomorphic Hardy spaces. Using these representations, we show these functions have boundary values in the sense of distributions that are representable by an atomic decomposition, and we show continuity of the Hilbert transform on this class of distributional boundary values.
Cite
@article{arxiv.2501.00542,
title = {An Atomic Representation for Bicomplex Hardy Classes},
author = {William L. Blair},
journal= {arXiv preprint arXiv:2501.00542},
year = {2025}
}
Comments
Many typographical/notational errors corrected from the last version