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

#### Abstract

Let $\alpha>0$ and $\gamma>0$. We consider integral operator of the form $${\mathcal{G}}_{\phi_\gamma}f(x):=\frac{1}{\Psi_\gamma (x)}\int_0^x (1-\frac{y}{x})^{\alpha-1}\phi_\gamma(y) f(y)dy \quad x>0.$$ 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.

#### Article information

Source
Adv. Oper. Theory, Volume 2, Number 3 (2017), 228-236.

Dates
Accepted: 30 March 2017
First available in Project Euclid: 4 December 2017

https://projecteuclid.org/euclid.aot/1512431673

Digital Object Identifier
doi:10.22034/aot.1701-1101

Mathematical Reviews number (MathSciNet)
MR3730051

Zentralblatt MATH identifier
06770923

#### Citation

Roohian, Homaion; Mohammadi Farsani, Soroosh. On the behavior at infinity of certain integral operator with positive kernel. Adv. Oper. Theory 2 (2017), no. 3, 228--236. doi:10.22034/aot.1701-1101. https://projecteuclid.org/euclid.aot/1512431673

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