Weighted Inequalities on John Domains

We study two-weighted inequalities on John domains. We first introduce domains that generalize the CŽ , M. domains defined by HajLasz and Koskela Ž J. London Math. Soc., to appear. and then show that our domains are actually just John domains. We then extend an interesting and nice result of HajLasz and Koskela by modifying their proof and then obtain some interesting consequences that include weighted Sobolev interpolation inequalities and an almost necessary and sufficient condition for two-weighted Poincar´e inequality on cubes.