Study of the maximal function and A_(p)-weights

Abstract

함수 Mf를 다음과 같이 정의하자. ◁그림삽입▷(원문을 참조하세요) 그러면 p를 1보다 큰 임의의 실수라 했을 때 Mf가 Strong-type (p, p)이기 위한 필요 충분조건이 A_(p)임을 증명한다.;This thesis is concerned with norm inequalities for the maximal function. We show that for 1 < P < ∞, the maximal function. ▷그림참조◁ is strong-type ( p, p) with respect to the weight w if and only if w∈A_(p), i.e., ▷그림참조◁ where

B

is the Lebesgue measure of B and the supremum is taken over all balls B.