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arXiv · 2501.00542

An Atomic Representation for Bicomplex Hardy Classes

William L. Blair
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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.

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BibTeXRIS

William L. Blair. 2024-12-31. An Atomic Representation for Bicomplex Hardy Classes. https://doi.org/10.1080/17476933.2025.2549391

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