This article continues to study the linearized Chandrasekhar equation. We use the Hilbert-type inequalities to accurately calculate the norm of the Fredholm integral operator and obtain the exact range for the parameters of the linearized Chandrasekhar equation to ensure that there is a unique solution to the equation in \(L^p\) space. A series of examples that can accurately calculate the norm of Fredholm integral operator shows that the Chandrasekhar kernel functions do not need to meet harsh conditions. As the symbolic part of the Chandrasekhar kernel function and the non-homogeneous terms satisfy the exponential decay condition, we yield a normed convergence rate of the approximation solution in \(L^p\) sense, which adds new results to the theory of radiation transfer in astrophysics.

中文翻译：

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具有尖锐边界的线性Chandrasekhar方程的存在性，唯一性和逼近解

本文继续研究线性化的Chandrasekhar方程。我们使用希尔伯特型不等式来精确计算Fredholm积分算子的范数，并获得线性Chandrasekhar方程参数的精确范围，以确保\（L ^ p \）空间中方程的唯一解。一系列可以准确计算Fredholm积分算子范数的例子表明，Chandrasekhar核函数不需要满足苛刻的条件。由于Chandrasekhar核函数的符号部分和非齐次项满足指数衰减条件，因此我们得出\（L ^ p \）中逼近解的赋范收敛速率 的意义，这为天体物理学的辐射传输理论增加了新的结果。