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Conjugate systems for harmonic functions over \(\mathbf Q_ p\). (Chinese. English summary) Zbl 1094.42025

Summary: A theory of \(p\)-adic conjugate systems for harmonic functions is proposed. Firstly, estimates for the Poisson kernel and its Hilbert transform are obtained, and their regularity properties are also shown. Moreover, estimates for derivatives of the Poisson kernel and its Hilbert transform are obtained. Then properties of boundary values of conjugate systems for harmonic functions are shown by using Poisson integrals. Lastly, Hardy spaces are constructed by using conjugate systems for harmonic functions.

MSC:

42B30 \(H^p\)-spaces
31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions
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