We prove sharp estimates for the renewal measure of a strongly nonlattice probability measure on the real line. In particular we consider the case where the measure has finite moments between 1 and 2. The proof uses Fourier analysis of tempered distributions.
"Estimates of the renewal measure." J. Math. Soc. Japan 73 (3) 681 - 701, July, 2021. https://doi.org/10.2969/jmsj/83298329