Abstract. Alexits' theorem is generalized to the case of $L^\infty $ space on the real line. Known results were obtained under additional restrictive assumptions. We avoid these by introducing a new analog of conjugate function.
AMS Subject Classification
(1991): 42A38
Keyword(s):
Alexits' theorem,
Fourier transform,
Hilbert transform,
conjugate function,
Lipschitz classes
Received July 17, 1997 and in revised form November 12, 1997. (Registered under 2654/2009.)
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