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May 27, 2026Open Access

Fredholmness of singular integral operators with continuous coefficients on Banach function spaces over the real line

MVMárcio ValenteUniversidade Nova de Lisboa

Key Points

This research aims to establish Fredholm criteria for singular integral operators on specific Banach function spaces.
Analysis of singular integral operators with continuous coefficients in rearrangement-invariant Banach spaces.
Focus on spaces with nontrivial Boyd indices and variable Lebesgue spaces.
Proved Fredholm criteria applicable to singular integral operators in the specified function spaces.
Identified characteristics of continuous coefficients influencing the criteria.

Abstract

Abstract We prove a Fredholm criteria for singular integral operators with continuous coefficients on any separable rearrangement-invariant Banach function space X (R) X (R) with nontrivial Boyd indices, and variable Lebesgue spaces with p () B₌ (R) p (·) ∈ B M (R).

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Márcio Valente (Mon,) studied this question.

synapsesocial.com/papers/6a168b160c924ddd1bd59e60 https://doi.org/https://doi.org/10.1007/s43036-026-00510-z

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