Abstract
In this note the class Lipα (t ) of continuous functions is introduced. The definition is arranged so that for the constant function α(t) ≡ α, the class Lipα (t ) is nothing but the classical Lipschitz space Lipα. Then, to justify that our set of axioms for α(t) are properly chosen, some celebrated theorems of Privalov, Titchmarsh, Hardy and Littlewood about Lipα functions are shown to be also valid for Lipα (t) functions.
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This work was supported by two research grants from NSERC (Canada) and FQRNT (Québec).
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Mashreghi, J. Generalized Lipschitz Functions. Comput. Methods Funct. Theory 5, 431–444 (2006). https://doi.org/10.1007/BF03321108
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DOI: https://doi.org/10.1007/BF03321108