Advances in Operator Theory

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

Homaion Roohian and Soroosh Mohammadi Farsani

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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

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

Received: 20 January 2017
Accepted: 30 March 2017
First available in Project Euclid: 4 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B38: Operators on function spaces (general)
Secondary: 47G10: Integral operators [See also 45P05] 47B34: Kernel operators

integral operators weighted Lebesgue space behavior at infinity convergence almost everywhere


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.

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