Estimates of \(L_p\) norms for sums of positive functions

Ilgiz Kayumov

Abstract


We present new inequalities of \(L_p\) norms for sums of positive functions. These inequalities are useful for investigation of convergence of simple partial fractions in \(L_p(\mathbb{R})\).


Keywords


Simple partial fractions; \(L_p\) estimates.

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References


Protasov, V. Yu., Approximation by simple partial fractions and the Hilbert transform, Izv. Math. 73 (2) (2009), 333–349.

Kayumov, I. R., Convergence of simple partial fractions in (L_p(mathbb{R})), Sb. Math. 202 (10) (2011), 1493–1504.

Hardy, G. H., Littlewood, J. E., Pólya, G., Inequalities, Cambridge University Press, Cambridge, 1934.




DOI: http://dx.doi.org/10.2478/v10062-012-0026-9
Date of publication: 2015-07-15 00:00:00
Date of submission: 2016-01-12 09:02:10


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