摘要
Let w E Am. In this paper, we introduce weighted-（p,q） atomicHardy spaces Hwp,q（Rn × Rm） for 0 〈 p ≤ 1, q 〉 qw and show that the weighted Hardy space Hwp（Rn × Rm） defined via Littlewood-Paley square functions coincides with Hwp,q（Rn × Rm） for 0 〈 p ≤ 1, q 〉 qw. As applications, we get a general principle on the Hwp（Rn × Rm to Lwp（Rn × Rm） boundedness and a boundedness criterion for two parameter singular integrals on the weighted Hardy spaces.
Let w E Am. In this paper, we introduce weighted-（p,q） atomicHardy spaces Hwp,q（Rn × Rm） for 0 〈 p ≤ 1, q 〉 qw and show that the weighted Hardy space Hwp（Rn × Rm） defined via Littlewood-Paley square functions coincides with Hwp,q（Rn × Rm） for 0 〈 p ≤ 1, q 〉 qw. As applications, we get a general principle on the Hwp（Rn × Rm to Lwp（Rn × Rm） boundedness and a boundedness criterion for two parameter singular integrals on the weighted Hardy spaces.
