Limiting weak-type behavior for the Riesz transform and maximal operator when λ → ∞
نویسندگان
چکیده
منابع مشابه
L and weak L estimates for the maximal Riesz transform and the maximal Beurling transform
We prove L estimates for the maximal Riesz transform in terms of the Riesz transform itself, for 1 < p ≤ ∞. We show that the corresponding weak L1 estimate fails for the maximal Riesz transform, but surprisingly does hold for the maximal Beurling transform.
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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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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 2007
ISSN: 0026-2285
DOI: 10.1307/mmj/1177681984