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arXiv · 2410.03670

Interpolation spaces of Besov hierarchical spaces and non-linearities defined by vertex K functional and grid topology

Qixiang Yang·Haibo Yang
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Abstract

In 1967, Peetre proposed to give a precise description of the real interpolation space for Besov hierarchical spaces $l^{s,q}(A)$. In 1974, Cwikel proved that the Lions-Peetre formula for $(l^{q_0}(A_0), l^{q_1}(A_1))_{\theta,r}$ have no reasonable generalization for any $r\neq q$. In this paper, we apply wavelets to transform the study of real interpolation space into {\bf the study of nonlinear functional structure and nonlinear topological structure}. We solve completely Peetre's longstanding open problem.

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Qixiang Yang, Haibo Yang. 2024-09-13. Interpolation spaces of Besov hierarchical spaces and non-linearities defined by vertex K functional and grid topology. https://arxiv.org/abs/2410.03670

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