Vol. 81, No. 1, 1979

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Approximate identities and pointwise convergence

Herbert Stanley Bear, Jr.

Vol. 81 (1979), No. 1, 17–27
Abstract

We give two additional conditlons on an approximate identity (or positive kernel) {Kα} which insure that fKα f a.e. if f L1 on the line or circle. Where the convolution defines a function on the disc or a half-plane, as for the Poisson kernels or heat kernels, then the theorem gives automatically the paths toward a boundary point along which pointwise convergence occurs.

Mathematical Subject Classification 2000
Primary: 31A10
Milestones
Received: 8 May 1978
Published: 1 March 1979
Authors
Herbert Stanley Bear, Jr.