Weighted norm inequalities for hardy-littlewood maximal function for some differentiation bases

Abstract

A_Ρ조건이 A _Ρ-ε조건임의 사실없이 Cubes와 One-parameter family of rectangles와 balls defined by a pseudo-metrics인 bases에 대해서 M_β가 L^Ρ에서 유계인 필요충분 조건은 A_Ρ조건임을 증명하고 또 dyadic cubes 일 때 two-weight 에 대해 생각한다. ; We show that M_β: L^p(ωdx) → L^p(ωdx) if and only if ω ∈ A_p, for 1<p<∞ is proved without using the factω ∈ A_p implies ω ∈ A_p-εe for some ε>0, for the basis of all cubes, the basis of one-parameter family of rectangles, and the basis of balls defined by a pseudo-metrics. Also we consider the two-weight case for the basis of dyadic cubes.