Weak convergence of measures and weak type $(1,q)$ of maximal convolution operators
نویسندگان
چکیده
منابع مشابه
Weak Convergence of Convolution Products of Probability Measures on Semihypergroups
Let S be a topological semihypergroup. As it is known for hypergroups, the lack of an algebraic structure on a semihypergroup pause a serious challenge in extending results from semigroups. We use the notion of concretization or pseudomultiplication, to prove some results on weak convergence of the sequence of averages of convolution powers of probability measures on topological semihypergroups...
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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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As shown in [A1], the lowest constants appearing in the weak type (1, 1) inequalities satisfied by the centered Hardy-Littlewood maximal operator associated to certain finite radial measures, grow exponentially fast with the dimension. Here we extend this result to a wider class of radial measures and to some values of p > 1. Furthermore, we improve the previously known bounds for p = 1. Roughl...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1986
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1986-0845974-2