b+_p(K)条件下的复测度鞅.pdf

F40F2r Vol.40, No. 2 1997k3 ACTA MATHEMATICA SINICA March, 1997 b+ (K) IM p n
tvyd (CzG Cz 430072) X Q    wu j l ψ ∈ L1  bejag dµ = ψdν  pk dµ e loc qz   e k   xu k ψ e b+ (K ) q  eoc  e (p, p )  p  (p, p )  f p b+ (K ) ∩ a1 (K ) q esi  e L2 r m Φ h ∞ r jag oc  si  l MR(1991) HC 60G42 JC O211.4 Martingales with Respect to Complex Measures with b+ (K ) Condition p Hou Youliang Liu Peide (Department of Mathematics, Wuhan University, Wuhan 430072, China) Abstract This paper discussed the complex measure dµ = ψdν where the complex valued function ψ ∈ L1 and some properties of conditional expectations and matin- loc gales with respect to the measure dµ. Then it proved that the maximal operators of the martingales are week (p, p ) bounded and strong (p, p ) bounded if ψ satisfies b+ (K ) p condition and that the square operators of the martingales are L2-bounded if ψ satisfies b+ (K ) ∩ a1 (K ) condition. ∞ Keywords Complex measure, Maximal operator, Square operator, Weight function 1991 MR Subject Classification 60G42 Chinese Library Classification O211.4 1 UP aNLIDBXsdnpCoifman-Jones-Semmes[1] npk NfAd L2 sWaU [2,3] aNaN Hp BXaN zZsW Φ znpaNmDn L2 (Rd , dx) j Skb T (b) JBnMaaNzRDsyGF (Ω, F , Fn , ν) sG σ- n σ- sMdN ψ ∈ L∞ fjay