Criteria for the coincidence of the kernel of a function with the kernels of its Riesz and Abel integral means

• Date: 1998
• Main Authors: Usenko, E. G., Усенко, Є. Г.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 1998
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4792
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We indicate criteria for the coincidence of the Knopp kernels K(f) K(A f), and K (R f) of bounded functions f(t); here, $$R_f \left( t \right) = \frac{1}{{P\left( x \right)}}\int\limits_{\left[ {0;\left. t \right)} \right.} {f\left( x \right)dP and A_f \left( t \right)} = \frac{1}{{\int_0^\infty {...