Abstract
For p ≥ 2 we obtain bounds for L p -norms of the Fourier transform of real parts of simple partial fractions. For even p our estimate is sharp. We also prove a new inequality for L p -norms of simple partial fractions which in some cases is stronger than the corresponding inequality obtained by V. Yu. Protasov.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. Yu. Protasov, “Approximation by Simple Partial Fractions and the Hilbert Transform,” Izv. Ross. Akad. Nauk. Ser.Matem. 73(2), 123–140 (2009).
V. I. Danchenko, “Convergence of Simple Partial Fractions in L p(ℝ),” Matem. Sborn. 201(7), 53–66 (2010).
P. A. Borodin, “Approximation by Simple Partial Fractions on Semi-Axis,” Matem. Sborn. 200(8), 25–44 (2009).
W. Beckner, “Inequalities in Fourier Analysis,” Ann.Math. 102(6), 159–182 (1975).
K. I. Babenko, “An Inequality in the Theory of Fourier Integrals,” Izv. Akad. Nauk SSSR. Ser.Matem. 25(4), 531–542 (1961).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © I.R. Kayumov, 2012, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, No. 4, pp. 33–45.
About this article
Cite this article
Kayumov, I.R. Integral bounds for simple partial fractions. Russ Math. 56, 27–37 (2012). https://doi.org/10.3103/S1066369X12040044
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066369X12040044