Pointwise limits for sequences of convolution operators
نویسندگان
چکیده
منابع مشابه
Convergence of Sequences of Convolution Operators
When (φn) is a sequence of positive functions in L1(R) such that the convolutions φn ? f converge in L1-norm to f for all f ∈ L1(R), then these convolutions may or may not converge almost everywhere too. There is always a subsequence (φnk ) such that at least φnk ? f converges almost everywhere to f for all f ∈ Lp(R), 1 < p < ∞. A special case of this is when the functions φn are the dilations ...
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ژورنال
عنوان ژورنال: Acta Mathematica
سال: 1965
ISSN: 0001-5962
DOI: 10.1007/bf02391777