zbMATH — the first resource for mathematics

Some inequalities of Hardy-Littlewood type. (English) Zbl 0816.42017
G. H. Hardy and J. E. Littlewood [J. Reine Angew. Math. 157, 141-158 (1927; JFM 53.0193.03)] proved some very important inequalities having particular significance in applications. Several theorems concerning convergence and summability of orthogonal series apply these well-known inequalities. In this paper some related results for quasi-monotonic sequences are given.

42C15 General harmonic expansions, frames
26D15 Inequalities for sums, series and integrals
Full Text: DOI
[1] N. K. Bari andS. B. Stečkin, Best approximation and differential properties of two conjugate functions (Russian),Trudy Moskov. Mat. Obshch.,5 (1956), 485–522.
[2] G. H. Hardy andJ. E. Littlewood, Elementary theorems concerning power series with positive coefficients and moment constants of positive functions,J. reine angew. Math.,157(1927), 141–158. · JFM 53.0193.03
[3] A. A. Konyushkov, Best approximation by trigonometric polynomials and Fourier coefficients (Russian),Math. Sb.,44(1958), 53–84.
[4] L. Leindler, Generalization of inequalities Hardy and Littlewood,Acta Sci. Math. (Szeged),31(1970), 279–285. · Zbl 0203.06103
[5] L. Leindler, Inequalities of Hardy-Littlewood type,Analysis Math.,2(1976), 117–123. · Zbl 0326.26009
[6] L. Leindler, Further sharpening of inequalities of Hardy and Littlewood,Acta Sci. Math. (Szeged),54(1990), 285–289. · Zbl 0726.26014
[7] E. T. Copson, Note on series of positive terms,J. London Math. Soc.,2(1927), 9–12, and3(1928), 49–51. · JFM 53.0184.04
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.