Volume 4,  Issue 1, 2003

Article 3

POWER-MONOTONE SEQUENCES AND INTEGRABILITY OF TRIGONOMETRIC SERIES

J. NÉMETH

BOLYAI INSTITUTE, 
UNIVERSITY OF SZEGED, 
ARADI VÉRTANÚK TERE 1.
6720 SZEGED, HUNGARY
E-Mail: nemethj@math.u-szeged.hu

Received 13 June, 2002; Accepted 20 September, 2002.
Communicated by: A. Babenko

ABSTRACT.   The theorem proved in this paper is a generalization of some results, concerning integrability of trigonometric series, due to R.P. Boas, L. Leindler, etc. This result can be considered as an example showing the utility of the notion of power-monotone sequences..
Key words:
Trigonometrical series, Integrability, Quasi power-monotone sequence.

2000 Mathematics Subject Classification:
42A32.

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Other papers in this issue

Some Integral Inequalities Involving Taylor's Remainder. II
Hillel Gauchman

Note on the Carleman's Inequality for a Negative Power Number
Thanh Long Nguyen, Vu Duy Linh Nguyen and Thi Thu Van Nguyen

Power-Monotone Sequences and Integrability of Trigonometric Series
J. Németh

Fixed Points and the Stability of Jensen's Functional Equation
Liviu Cadariu and Viorel Radu

New Concepts of Well-Posedness for Optimization Problems with Variational Inequality Constraint
Imma Del Prete, M. Beatrice Lignola and Jacqueline Morgan

Relatively B-Pseudomonotone Variational Inequalities Over Product of Sets
Qamrul Hasan Ansari and Zubair Khan

On Multidimensional Ostrowski and Grüss Type Finite Difference Inequalities
B.G. Pachpatte

Bounded Linear Operators in Probabilistic Normed Space
Iqbal H. Jebril and Radhi Ibrahim M. Ali

Fundamental Inequalities on Firmly Stratified Sets and Some Applications
Serge Nicaise and Oleg M. Penkin

Partitioned Cyclic Functional Equations
Jae-Hyeong Bae and Won-Gil Park

Extensions of Popoviciu's Inequality Using a General Method
A. McD. Mercer

The Analytic Domain in the Implicit Function Theorem
H.C. Chang, W. He and N. Prabhu

Hadamard-type Inequalities for Quasiconvex Functions
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Iterative Schemes to Solve Nonconvex Variational Problems
Messaoud Bounkhel, Lotfi Tadj and Abdelouahed Hamdi

A Bound on the Deviation Probability for Sums of Non-Negative Random Variables
Andreas Maurer

Hilbert-Pachpatte Type Integral Inequalities and their Improvement
S.S. Dragomir and Young-Ho Kim

Coefficient Inequalities for Certain Classes of Meromorphically Starlike and Meromorphically Convex Functions
Shigeyoshi Owa and Nicolae N. Pascu

Second-order Differential Proximal Methods for Equilibrium Problems
A. Moudafi

Some Integral Inequalities Related to Hilbert's
T.C. Peachey

Comments on Some Analytic Inequalities
Ilko Brnetic and Josip Pecaric

On Entire and Meromorphic Functions that Share Small Functions with their Derivatives
Kit-Wing Yu

Comparison of Green Functions for Generalized Schrödinger Operators on C1,1-Domains
Lotfi Riahi

Erdős-Turán Type Inequalities
Laurentiu Panaitopol

Some Variants of Anderson's Inequality in C1-Classes
Salah Mecheri and Messaoud Bounkhel
 

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