Integral bounds for simple partial fractions

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. © Allerton Press, Inc., 2012.