Computational Methods and Function Theory 5 (2005), No. 2, 431--444
Copyright Heldermann Verlag 2005
Javad Mashreghi
javad.mashreghi@mat.ulaval.ca , Département de mathématiques et de statistique, Université Laval, Québec, QC, G1K 7P4, Canada.
In this note the class $\Lip_{\alpha(t)}$ of continuous functions is introduced. The definition is arranged so that for the constant function $\alpha(t) \equiv \alpha$, the class $\Lip_{\alpha(t)}$ is nothing but the classical Lipschitz space $\Lip_\alpha$. Then, to justify that our set of axioms for $\alpha(t)$ are properly chosen, some celebrated theorems of Privalov, Titchmarsh, Hardy and Littlewood about $\Lip_\alpha$ functions are shown to be also valid for $\Lip_{\alpha(t)}$ functions.
Keywords: Lipschitz functions, test function, associated test function, Hilbert transform, Hardy classes.
MSC 2000: Primary 26A16; Secondary 32A40.
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