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.
متن کامل-boundedness of the Hilbert transform
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...
متن کاملA Note on the Hilbert Transform
If /(OG^P) £>!> then f(x)^Lpy and a considerable literature is devoted to studying the relationship of such pairs of "conjugate" functions to the theory of functions analytic in a half-plane. More to the point of the present note is a series of papers studying the Hubert transform along strictly real variable lines ([2, 3 ] ; further bibliography in [2]). Much less is known about f(x) when f(t)...
متن کاملThe Number Theoretic Hilbert Transform
Abstract This paper presents a general expression for a number-theoretic Hilbert transform (NHT). The transformations preserve the circulant nature of the discrete Hilbert transform (DHT) matrix together with alternating values in each row being zero and non-zero. Specific examples for 4point, 6-point, and 8-point NHT are provided. The NHT transformation can be used as a primitive to create cry...
متن کاملOn the Bilinear Hilbert Transform
In joint work with C. Thiele, the author has shown that A. Calderón’s bilinear Hilbert transform extends to a bounded operator on certain products of L spaces. This article illustrates the method of proof by giving a complete proof of an inequality which is slightly weaker than the original conjecture of Calderón concerning this transform. 1991 Mathematics Subject Classification: 42A50
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ژورنال
عنوان ژورنال: Journal d'Analyse Mathématique
سال: 2010
ISSN: 0021-7670,1565-8538
DOI: 10.1007/s11854-010-0017-0