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We show that if a symbol \(a\in S_{1,0}^0\) slowly oscillates at infinity in the first variable, then the condition \(\displaystyle \lim _{R\to \infty }\inf _{|x|+|\xi |\ge R}|a(x,\xi )|>0 \) is sufficient for the Fredholmness of the pseudodifferential operator \(\operatorname {Op}(a)\) on a separable rearrangement-invariant Banach function space \(X(\mathbb {R}^d)\) , whose Boyd indices satisfy \(0<\alpha _X\) and \(\beta _X<1\) .

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Fredholmness of Pseudodifferential Operators on Rearrangement-Invariant Spaces

  • 会议论文

  • 发表日期：

    2025年

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  • Oleksiy Karlovych

摘要

We show that if a symbol \(a\in S_{1,0}^0\) slowly oscillates at infinity in the first variable, then the condition \(\displaystyle \lim _{R\to \infty }\inf _{|x|+|\xi |\ge R}|a(x,\xi )|>0 \) is sufficient for the Fredholmness of the pseudodifferential operator \(\operatorname {Op}(a)\) on a separable rearrangement-invariant Banach function space \(X(\mathbb {R}^d)\) , whose Boyd indices satisfy \(0<\alpha _X\) and \(\beta _X<1\) .