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arXiv · 2501.00631

Boundedness of Harmonic Conjugation on Weighted Bergman Spaces

Timothy Ferguson
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Abstract

We prove that if a weight is a Bekoll\'{e}-Bonami weight for some $q$ and it satisfies another simple condition that depends on $0 < p < \infty$, then the operator taking a function to its harmonic conjugate is bounded on the harmonic Bergman space $a^p$. One part of our results uses a certain special type of good lambda inequality.

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Timothy Ferguson. 2024-12-31. Boundedness of Harmonic Conjugation on Weighted Bergman Spaces. https://arxiv.org/abs/2501.00631

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