Multiple conjugate functions and multiplicative Lipschitz classes
Ferenc Móricz
Colloquium Mathematicae, Tome 116 (2009), p. 21-32 / Harvested from The Polish Digital Mathematics Library
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We extend the classical theorems of I. I. Privalov and A. Zygmund from single to multiple conjugate functions in terms of the multiplicative modulus of continuity. A remarkable corollary is that if a function f belongs to the multiplicative Lipschitz class Lip(α₁,...,αN) for some 0<α₁,...,αN<1 and its marginal functions satisfy f(·,x₂,...,xN)∈Lipβ₁,...,f(x₁,...,xN-1,·)∈LipβN for some 0<β₁,...,βN<1 uniformly in the indicated variables xl, 1 ≤ l ≤ N, then f̃(η₁,...,ηN)∈Lip(α₁,...,αN) for each choice of (η₁,...,ηN) with ηl=0 or 1 for 1 ≤ l ≤ N.

Publié le : 2009-01-01
EUDML-ID : urn:eudml:doc:283958 
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     year = {2009},
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Ferenc Móricz. Multiple conjugate functions and multiplicative Lipschitz classes. Colloquium Mathematicae, Tome 116 (2009) pp. 21-32. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm115-1-3/