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Convolution operators induced by approximate identities and pointwise convergence in spaces

Authors:	Parthena Avramidou

Institution:	Department of Mathematics, Ohio State University, Columbus, Ohio 43210

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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