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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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


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