A characterization of the Hilbert transform
نویسندگان
چکیده
منابع مشابه
The Hilbert Transform of a Measure
Let e be a homogeneous subset of R in the sense of Carleson. Let μ be a finite positive measure on R and Hμ(x) its Hilbert transform. We prove that if limt→∞ t|e ∩ {x | |Hμ(x)| > t}| = 0, then μs(e) = 0, where μs is the singular part of μ.
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The Hilbert transform is essentially the only singular operator in dimension 1. This undoubtedly makes it one of the the most important linear operators in harmonic analysis. The Hilbert transform has had a profound bearing on several theoretical and physical problems across a wide range of disciplines; this includes problems in Fourier convergence, complex analysis, potential theory, modulatio...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1998
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-98-04214-2