Convolution operators induced by approximate identities and pointwise convergence in 𝐿_{𝑝}(ℝ) spaces

Avramidou, Parthena

doi:10.1090/S0002-9939-04-07494-5

Convolution operators induced by approximate identities and pointwise convergence in $L_p(\mathbb {R})$ spaces
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Proc. Amer. Math. Soc. 133 (2005), 175-184 Request permission

Abstract:

Given a sequence of kernels $\phi _n$ for which the operators $T_nf=\phi _n\ast f$ converge a.e. in all $L_p(\mathbb {R})$ spaces, $p\geq 1$, a perturbation method is provided with the property that the modified convolution operators converge pointwise only in selective spaces.

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