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Abel summability of
conjugate integrals
S. P. Philipp |
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Vol. 44 (1973), No. 2, 693–700
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Abstract |
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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
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Milestones
Received: 3 March 1971
Published: 1 February 1973
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Authors |
| S. P. Philipp | |
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