Weighted inequalities for Hilbert transforms and multiplicators of Fourier transforms

Weighted inequalities for Hilbert transforms and multiplicators of Fourier transforms

As is well known, invariant operators with a shift can be bounded from Lp into Lq only if 1<p≤q<∞. We show that the case q<p might also hold for weighted spaces. We derive the sufficient conditions for the validity of strong (weak) (p,q) type inequalities for the Hilbert transform...

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Bibliographic Details
Main Authors: A. Meskhi, V. Kokilashvili
Format: Article
Language:English
Published: SpringerOpen 1997-01-01
Series:Journal of Inequalities and Applications
Subjects:
Hilbert transform; two-weight inequality; weak and strong type estimates; Fourier transform; multiplier.
Online Access:http://dx.doi.org/10.1155/S1025583497000167
Description
Summary:As is well known, invariant operators with a shift can be bounded from Lp into Lq only if 1<p≤q<∞. We show that the case q<p might also hold for weighted spaces. We derive the sufficient conditions for the validity of strong (weak) (p,q) type inequalities for the Hilbert transform when 1<q<p<∞ (q=1,1<p<∞).
ISSN:1025-5834
1029-242X

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