Soichiro SUZUKI

Identities and inequalities for integral transforms involving squares of the Bessel functions

We consider an integral transform given by Tνf(s):=π∫0∞rsJν(rs)2f(r) dr, where Jν denotes the Bessel function of the first kind of order ν. As shown by Walther (2002), this transform plays an essential role in the study of optimal constants of smoothing estimates for the free Sch...