Fredholm theorems for integral equations in $L^p$ spaces

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发表日期：

2026年7月24日

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Sheng-Ya Feng,
Der-Chen Chang

摘要

For the Fredholm integral equations of the second kind, this paper introduces the mixed norm condition for kernel functions and establishes the Fredholm theory on $L^p$ $L^{p}$ spaces ( $1 \leqslant p \leqslant \infty $ $1 ⩽ p ⩽ \infty$ ) by means of the degenerate kernel approximation method. The research method in this paper frees the study of Fredholm integral equations of the second kind from the limitation of Hilbert spaces and is widely applicable to other function spaces represented by $L^p$ $L^{p}$ spaces (usually Banach spaces), which provides important theoretical support for the research on operator theory and related mathematical physics problems. Since the obtained results are independent of the specific properties of the real line, all conclusions can be directly generalized to high-dimensional Euclidean spaces, offering a reliable theoretical basis for the analysis of high-dimensional integral equations.

Fredholm theorems for integral equations in \(L^p\) spaces

摘要