## Advances in Operator Theory

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

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

Homaion Roohian and Soroosh Mohammadi Farsani

#### 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**

Received: 20 January 2017

Accepted: 30 March 2017

First available in Project Euclid: 4 December 2017

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.22034/aot.1701-1101

**Mathematical Reviews number (MathSciNet)**

MR3730051

**Zentralblatt MATH identifier**

06770923

**Subjects**

Primary: 47B38: Operators on function spaces (general)

Secondary: 47G10: Integral operators [See also 45P05] 47B34: Kernel operators

**Keywords**

integral operators weighted Lebesgue space behavior at infinity convergence almost everywhere

#### 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