We present new inequalities of Lp norms for sums of positive functions. These inequalities are useful for investigation of convergence of simple partial fractions in Lp(ℝ).
@article{bwmeta1.element.doi-10_2478_v10062-012-0026-9,
author = {Ilgiz Kayumov},
title = {
Estimates of L
p
norms for sums of positive functions
},
journal = {Annales UMCS, Mathematica},
volume = {67},
year = {2013},
pages = {11-16},
zbl = {1285.28016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10062-012-0026-9}
}
Ilgiz Kayumov.
Estimates of L
p
norms for sums of positive functions
. Annales UMCS, Mathematica, Tome 67 (2013) pp. 11-16. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10062-012-0026-9/
[1] Protasov, V. Yu., Approximation by simple partial fractions and the Hilbert transform, Izv. Math. 73 (2) (2009), 333-349.[WoS] | Zbl 1178.41010
[2] Kayumov, I. R., Convergence of simple partial fractions in Lp(R), Sb. Math. 202 (10) (2011), 1493-1504.[WoS] | Zbl 1244.30003
[3] Hardy, G. H., Littlewood, J. E., Pólya, G., Inequalities, Cambridge University Press, Cambridge, 1934.