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## Main Question or Discussion Point

let be the integral equation

[tex] h(x)= \int_{0}^{\infty} \frac{dy}{y}K(y/x)f(y) [/tex]

here the kernel is always a positive , then if [tex] h(x)=O(x^{a}) [/tex] and the integral

[tex] \int_{0}^{\infty} \frac{dy}{y}K(y)y^{a} [/tex] exists and is a positive real number then also [tex] f(x)= O(x^{a}) [/tex]

[tex] h(x)= \int_{0}^{\infty} \frac{dy}{y}K(y/x)f(y) [/tex]

here the kernel is always a positive , then if [tex] h(x)=O(x^{a}) [/tex] and the integral

[tex] \int_{0}^{\infty} \frac{dy}{y}K(y)y^{a} [/tex] exists and is a positive real number then also [tex] f(x)= O(x^{a}) [/tex]