Roohian, H., Mohammadi Farsani, S. (2017). On the behavior at infinity of certain integral operator with positive kernel. Advances in Operator Theory, 2(3), 228-236. doi: 10.22034/aot.1701-1101

Homaion Roohian; Soroosh Mohammadi Farsani. "On the behavior at infinity of certain integral operator with positive kernel". Advances in Operator Theory, 2, 3, 2017, 228-236. doi: 10.22034/aot.1701-1101

Roohian, H., Mohammadi Farsani, S. (2017). 'On the behavior at infinity of certain integral operator with positive kernel', Advances in Operator Theory, 2(3), pp. 228-236. doi: 10.22034/aot.1701-1101

Roohian, H., Mohammadi Farsani, S. On the behavior at infinity of certain integral operator with positive kernel. Advances in Operator Theory, 2017; 2(3): 228-236. doi: 10.22034/aot.1701-1101

On the behavior at infinity of certain integral operator with positive kernel

Receive Date: 20 January 2017,
Revise Date: 30 March 2017,
Accept Date: 30 March 2017

Abstract

Let $\alpha>0$ and $\gamma>0$. We consider integral operator of the form $$ {\mathcal{G}}_{\phi_\gamma}f(x):=\frac{1}{\Psi_\gamma (x)}\int_0^x (1-\frac{y}{x})^{\alpha-1}\phi_\gamma(y) f(y)dy,\,\,\,\, x>0. $$ This paper is devoted to the study of the infinity behavior of ${\mathcal{G}}_{\phi_\gamma}$. We also provide separately result on the similar problem in the weighted Lebesgue space.