Sharp Bounds for t-Haar Multipliers on L2

摘要

Assume t ? R， the weight w ∈ C_(2t)~d and there is q > 1 such that w~(2t) ∈ A_q~d. We show that the L~2-norm of the t-Haar multiplier of complexity (m, n) associated to w depends on the square root of the C_(2t)~d-characteristic of w times the square root of the A_q~d-characteristic of w2t times a constant that depends polynomially on the complexity. In particular, if w ∈ C_(2t)~d ∩ A_∞~s then w~(2t) ∈ A_q~d for some q > 1 and the conditions are satisfied.