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<p>We prove a Fredholm criteria for singular integral operators with continuous coefficients on any separable rearrangement-invariant Banach function space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(X(\mathbb {R})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>X</mi> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">R</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> with nontrivial Boyd indices, and variable Lebesgue spaces with <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(p(\cdot )\in \mathcal {B}_{M}(\mathbb {R})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mrow> <mo stretchy="false">(</mo> <mo>·</mo> <mo stretchy="false">)</mo> </mrow> <mo>∈</mo> <msub> <mi mathvariant="script">B</mi> <mi>M</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">R</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>.</p>

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

  • 期刊论文

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  • 发表日期：

    2026年5月25日

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  • Márcio Valente

摘要

We prove a Fredholm criteria for singular integral operators with continuous coefficients on any separable rearrangement-invariant Banach function space \(X(\mathbb {R})\) X ( R ) with nontrivial Boyd indices, and variable Lebesgue spaces with \(p(\cdot )\in \mathcal {B}_{M}(\mathbb {R})\) p ( · ) ∈ B M ( R ) .