Weighted inequalities for the generalized maximal operator in martingale spaces

Abstract

The generalized maximal operator M in martingale spaces is considered. For 1 < p ≤ q < ∞, the authors give a necessary and sufficient condition on the pair (\hat \mu , v) for M to be a bounded operator from martingale space L ^p(v) into L ^q(\hat \mu ) or weak-L ^q (\hat \mu ), where \hat \mu is a measure on Ω × ℕ and v a weight on Ω. Moreover, the similar inequalities for usual maximal operator are discussed.

Keywords

Martingale / Maximal operator / Weighted inequality / Carleson measure

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