The integral representations of the products for the harmonic polynomials and the Poisson kernel and their growth properties in the half space

Yanhui ZHANG; Guantie DENG; Kangli YANG

doi:10.3868/s140-DDD-026-0002-x

Front. Math. China ›› 2026, Vol. 21 ›› Issue (1) :15 -21. DOI: 10.3868/s140-DDD-026-0002-x

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The integral representations of the products for the harmonic polynomials and the Poisson kernel and their growth properties in the half space

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Abstract

In this paper, we study the integrals and growth properties of the products multiplying types of polynomials and the Poisson kernel in the half space. By gradually weakening the convergence conditions and redefining the measure, two special cases, namely the growth properties of the integrals multiplying two types of harmonic polynomials and the Poisson kernel, are obtained to solve the Dirichlet boundary value problem of the polyharmonic equation. Moreover, we generalize the results concerning the modified Poisson integral in the half space.

Keywords

Harmonic polynomial / growth property / modified Poisson kernel

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Yanhui ZHANG, Guantie DENG, Kangli YANG. The integral representations of the products for the harmonic polynomials and the Poisson kernel and their growth properties in the half space. Front. Math. China, 2026, 21(1): 15-21 DOI:10.3868/s140-DDD-026-0002-x

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