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2-Local isometries on vector-valued differentiable functions

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Abstract

Let Q, K be connected open subsets of \(\mathbb {R}^m\) and A(X), A(Y) be some kind of function spaces. We will study the 2-local isometries between the vector-valued differentiable function spaces \(C_0^p(Q, A(X))\) and \(C_0^p(K, A(Y))\), and show that they can be written as weighted composition operators.

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Acknowledgements

We would like to express our gratitude to the anonymous referee for many constructive comments and suggestions to improve the final form of the paper. This work is partly supported by NSF of China (12171251)

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Authors and Affiliations

  1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, China

    Lei Li & Siyu Liu

  2. School of Mathematics, Tianjin University, Tianjin, 300354, China

    Weiyun Ren

Authors
  1. Lei Li
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  2. Siyu Liu
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  3. Weiyun Ren
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Correspondence to Lei Li.

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Communicated by Vesko Valov.

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Li, L., Liu, S. & Ren, W. 2-Local isometries on vector-valued differentiable functions. Ann. Funct. Anal. 14, 70 (2023). https://doi.org/10.1007/s43034-023-00295-9

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  • DOI: https://doi.org/10.1007/s43034-023-00295-9

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