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2002/2003 Difference functions of periodic \(L_p\) functions.
Tamás Mátrai
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Real Anal. Exchange 28(2): 355-374 (2002/2003).


We examine for which sets \(H\) of the circle group \(\mathbb{R} / \mathbb{Z}\) can the difference functions \(f(x+h)- f(x)\) of a measurable or \(L_{p}\) function \(f\) belong to an \(L_{q}\) class for every \(h \in H\) without \(f\) itself being in \(L_{q}\). Tamás Keleti conjectured in \cite{Elek1} that these sets are the \(N\)-sets; that is, the sets of absolute convergence of Fourier-series. We prove this conjecture for \(q \leq 2\). For \(q=2\), as a quantitative analogue of this statement, we prove a minimax theorem.


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Tamás Mátrai. "Difference functions of periodic \(L_p\) functions.." Real Anal. Exchange 28 (2) 355 - 374, 2002/2003.


Published: 2002/2003
First available in Project Euclid: 20 July 2007

zbMATH: 1049.28003
MathSciNet: MR2009759

Primary: 28A99 , 42A20

Keywords: $L_p$ function , $N$-set , difference function

Rights: Copyright © 2002 Michigan State University Press

Vol.28 • No. 2 • 2002/2003
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