I don't know, but since the yellow sun gives Superman his power, it's only logical that the effects of Kryptonite only affect Superman where he has his powers. Kryptonite since it is radioactive seems to affect the powers Superman has, since the first thing it does is take them away. They are basically human on Krypton, so why would it affect them in the same way it would when they have powers on earth or with another yellow sun?
I realize that different continuities might deal with Kryptonite differently, but I remember once when Superman was stranded on a planet with a red sun he had no powers and kryptonite didn't affect him.
I guess there is a lot of discussion on this matter. It seem some people think the yellow sun is the reason Kryptonite weakens him and others feel otherwise. Just read this on a Superman board.
"... The yellow sun juices him up, but the green kryptonite interacts with our sun's radiation and within a certain radius it negates the effect."
I just read somewhere else that the effect of Kryptonite is only amplified by the yellow sun's effect on Superman. So a regular Kryptonian would not be affected the same way without a yellow sun.