Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 17, No. 2, pp. 101-105 (2001)

Note on the converses of inequalities of Hardy and Littlewood

József Németh

Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720 Szeged, Hungary}

Abstract: The inequalities of Hardy-Littlewood type play very important role in many theorems concerning convergence or summability of orthogonal series. In the applications many times their converses are also very useful. Both the original inequalities and their converses have been generalized in several directions by many authors, among others Leindler (see [5], [6], [7], [8]), Mulholland (see [10]), Chen Yung-Ming (see [1]), etc.

The aim of this paper is to give further generalization of the inequalities of converse type replacing the power functions by more general ones.

Keywords: Hardy-Littlewood inequalities, quasi monotone sequences.

Classification (MSC2000): 26D15; 40A05

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