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Bo-Yong Long

Publications and source records attributed to Bo-Yong Long.

4 recordsLinked to original sources
arXiv2024

Boundary behavior of alppha-harmonic functions and their Riesz-Fejer inequalities

The solutions of a kind of second-order homogeneous partial differential equation are called (real kernel) alpha-harmonic functions. In this paper, the boundary correspondence and boundary behavior of alpha-harmonic functions are studied, and the corresponding Dirichlet problem is solved. As one of its applications, an asymptotic optimal Riesz-Fejer inequality for alpha-harmonic functions is obtained. In addition, the subharmonic properties of alpha-harmonic functions is explored and an optimal radius is obtained.

math.CV↗
arXiv2024

Some optimal inequalities for alpha-harmonic functions estimated by their boundary functions

The solutions of a kind of second-order homogeneous partial differential equation are called (real kernel) alpha-harmonic functions. The alpha-harmonic functions and their first-order partial derivative functions on unit disk are estimated using the $L^p$ norm of the boundary functions of the alpha-harmonic functions. A series of inequalities are obtained. In addition, when the alpha-harmonic functions are quasiconformal, their first-order partial derivative functions are estimated by the arc length of the domain boundary and the Lipschitz constant of the boundary functions. All of the inequalities obtained in this article are optimal or asymptotically optimal.

math.CV↗
arXiv2024

Several properties of a class of generalized harmonic mappings

We call the solution of a kind of second order homogeneous partial differential equation as real kernel alpha-harmonic mappings. In this paper, the representation theorem, the Lipschitz continuity, the univalency and the related problems of the real kernel alpha-harmonic mappings are explored.

math.CV↗