Superposition operator problems of Hölder-Lipschitz spaces

• Autorzy: Niu Yeli , Wang Heping

Identyfikatory

DOI

10.1515/dema-2024-0043

• Języki publikacji: EN

Abstrakty

EN

Let 𝑓 be a function defined on the real line, and 𝑇𝑓 be the corresponding superposition operator which maps ℎ to 𝑇𝑓 (ℎ) , i.e., 𝑇𝑓(ℎ) =𝑓 ∘ℎ . In this article, the sufficient and necessary conditions such that 𝑇𝑓 maps periodic Hölder-Lipschitz spaces 𝐻𝛼𝑝 into itself with 0 <𝛼 <1/𝑝 and 1/𝑝 <𝛼 <1 , where 𝛼 is the smoothness index, are shown. Our result in the case 0 <𝛼 <1/𝑝 may be the first result about the superposition operator problems of smooth function space containing unbounded functions.

Słowa kluczowe

EN

Hölder-Lipschitz spaces; superposition operator problem; locally Lipschitz function; Lipschitz function

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2024
• Tom: Vol. 57, nr 1
• Strony: art. no. 20240043
• Opis fizyczny: Bibliogr. 15 poz., rys.

Twórcy

autor

Niu Yeli

• Department of Mathematics, Shanghai Normal University, Shanghai, 200234, P. R. China

autor

Wang Heping

• School of Mathematical Sciences, BCMIIS, Capital Normal University, Beijing 100048, P. R. China

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2026).