Limiting Weak–type Behavior for Singular Integral and Maximal Operators
نویسنده
چکیده
The following limit result holds for the weak–type (1,1) constant of dilation-commuting singular integral operator T in Rn: for f ∈ L1(Rn), f ≥ 0, lim λ→0 λ m{x ∈ R : |Tf(x)| > λ} = 1 n ∫ Sn−1 |Ω(x)|dσ(x)‖f‖1. For the maximal operator M , the corresponding result is lim λ→0 λ m{x ∈ R : |Mf(x)| > λ} = ‖f‖1.
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