Multiple conjugate functions and multiplicative Lipschitz classes

• Autorzy: Ferenc Móricz
• Języki publikacji: EN

Abstrakty

EN

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 $Lip(α₁,..., α_N)$ for some $0 < α₁,...,α_N < 1$ and its marginal functions satisfy $f(·,x₂,...,x_N) ∈ Lip β₁,...,f(x₁,...,x_{N-1},·) ∈ Lip β_N$ for some $0 < β₁,...,β_N < 1$ uniformly in the indicated variables $x_{l}$, 1 ≤ l ≤ N, then $f̃^{(η₁, ..., η_N)} ∈ Lip(α₁, ..., α_N)$ for each choice of $(η₁,...,η_N)$ with $η_{l} = 0$ or 1 for 1 ≤ l ≤ N.

Kategorie tematyczne

• 42B05: Fourier series and coefficients
• 42A50: Conjugate functions, conjugate series, singular integrals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2009
• Tom: 115
• Numer: 1
• Strony: 21-32

Daty

wydano

2009

Twórcy

autor

Ferenc Móricz

• Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary

Identyfikatory

DOI

10.4064/cm115-1-3