Vol. 44, No. 2, 1973

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Abel summability of conjugate integrals

S. P. Philipp

Vol. 44 (1973), No. 2, 693–700
Abstract

It is proved here that the conjugate Fourier-Stieltjes integral of a finite-valued Borel measure μ on Euclidean k-space, k 1, taken with respect to a Calderon-Zygmund kernel in Lip α,0 < α < 1, is almost everywhere (with respect to Lebesgue measure) Abel summable to the conjugate function of μ taken with respect to the above mentioned kernel. This has been already established for k 8 and for k even.

Mathematical Subject Classification
Primary: 42A92
Secondary: 44A25, 42A40
Milestones
Received: 3 March 1971
Published: 1 February 1973
Authors
S. P. Philipp