Hilbert transform on $W_{\sigma}^1$
نویسندگان
چکیده
منابع مشابه
On 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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The use of the Hilbert transform for time/frequency analysis of signals is briefly considered. While the Hilbert transform is based on arbitrary continuous signals, most practical signals are digitially sampled and time-limited. To avoid aliasing in the sampling process the signals must also be bandlimited. It is argued that it is reasonable to consider such sampled signals as periodic (this is...
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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)...
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For any dimension n ≥ 2, we consider the maximal directional Hilbert transform HU on R associated with a direction set U ⊆ Sn−1: HUf(x) := 1 π sup v∈U ∣∣∣p.v.∫ f(x− tv) dt t ∣∣∣. The main result in this article asserts that for any exponent p ∈ (1,∞), there exists a positive constant Cp,n such that for any finite direction set U ⊆ Sn−1, ||HU ||p→p ≥ Cp,n √ log #U, where #U denotes the cardinali...
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ژورنال
عنوان ژورنال: Matematychni Studii
سال: 2019
ISSN: 1027-4634
DOI: 10.30970/ms.52.1.32-37