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Extension and embedding theorems for Campanato spaces on C0,γ$C^{0,\gamma }$ domains

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  • Damiano Greco
  • Pier Domenico Lamberti

Abstract

We consider Campanato spaces with exponents λ,p$\lambda, p$ on domains of class C0,γ$C^{0,\gamma }$ in the N‐dimensional Euclidean space endowed with a natural anisotropic metric depending on γ$\gamma$. We discuss several results including the appropriate Campanato's embedding theorem and we prove that functions of those spaces can be extended to the whole of the Euclidean space without deterioration of the exponents λ,p$\lambda, p$.

Suggested Citation

  • Damiano Greco & Pier Domenico Lamberti, 2024. "Extension and embedding theorems for Campanato spaces on C0,γ$C^{0,\gamma }$ domains," Mathematische Nachrichten, Wiley Blackwell, vol. 297(6), pages 2047-2066, June.
    • Handle: RePEc:bla:mathna:v:297:y:2024:i:6:p:2047-2066
    DOI: 10.1002/mana.202300092
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    References listed on IDEAS

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    1. Maria Stella Fanciullo & Pier Domenico Lamberti, 2017. "On Burenkov's extension operator preserving Sobolev–Morrey spaces on Lipschitz domains," Mathematische Nachrichten, Wiley Blackwell, vol. 290(1), pages 37-49, January.
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