分数次积分算子的弱型极限行为

Limiting weak-type behavior for fractional integral operators

将分别建立当λ→0和λ→+∞时,分数次积分算子的弱型极限行为.具体来说:对于任意的f∈L1(Rn),有下面2个等式成立,limλ→0λ|{x∈R^n:|I_αf|>λ}|^((n-α)/n)=v_n^((n-α)/n)‖f‖1,limλ→+∞λ|{x∈R^n:|I_αf|>λ}|^((n-α)/n)=0.

In this paper,we establish the limiting weak type behaviors for fractional integral whenλ→0andλ→∞ separately.More specifically,for any f∈L1（Rn）,there holds limλ→0λ｜{x∈Rn：｜Iαf｜〉λ}｜（n-α）/n=vn（n-α）/n‖f‖1,limλ→＋∞λ｜{x∈Rn：｜Iαf｜〉λ}｜（n-α）/n=0.