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Conjugate systems for temperatures over \(\mathbb{Q}_p\). (Chinese. English summary) Zbl 1069.44006

Summary: A theory of \(p\)-adic conjugate systems for temperatures is presented. First of all, estimations for the heat kernel and its Hilbert transform are obtained, and their regularity properties are also shown. Moreover, estimations on the derivatives of the heat kernel and its Hilbert transform are obtained. Then, properties of boundary values of the conjugate systems for temperatures are shown by Gauss integrals. Last, Hardy spaces are constructed by these conjugate systems.

MSC:

44A15 Special integral transforms (Legendre, Hilbert, etc.)
35K05 Heat equation
35A22 Transform methods (e.g., integral transforms) applied to PDEs
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