Abstract
In this paper weighted Fourier inequalities are established with weights in the Ap-class of Muckenhoupt. Specifically, for even, non-decreasing weights on (0, ∞) the weight conditions are necessary and sufficient for the Paley-Titchmarsh inequality and its extensions. For decreasing weights the inequalities fail.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
J.J. Benedetto and H.P. Heinig, Weighted Hardy spaces and the Laplace transform. Harmonic Anal. Conf., Cortona, Italy, 1982. Lect. Notes in Math. 992, Springer Verlag,xxx 240–277.
J.J. Benedetto, H.P. Heinig and R. Johnson, Weighted Hardy spaces and the Laplace transform II. Math. Nachr. (to appear).
J.S. Bradley, Hardy inequalities with mixed norms. Canad. Math. Bull. 25 (1978), 405–408.
G.H. Hardy and J.E. Littlewood, Some new properties of Fourier constants. Math. Ann. 97 (1926–27), 159–209.
R. Hunt, B. Muckenhoupt and R. Wheeden, Weighted norm inequalities for the conjugate function and Hilbert transform. Trans. Amer. Math. Soc. 176 (1973), 227–251.
S. Igari, Some integrability theorems of trigonometric series and monotone decreasing functions. Tohoku Math. J. 12 (1) (1960), 139–146.
P.G. Rooney, Generalized HP-spaces and Laplace transforms. Abstract spaces and approximation. In: P.L. Butzer and B.Sz. Nagy (ed.), Proc. Conf. Oberwolfach, 1966, 258–269.
C. Sadosky and R.L. Wheeden, Some weighted norm inequalities for the Fourier transform of functions with vanishing moments. Manuscript (18 pages).
E.M. Stein, Interpolation of linear operators. Trans. Amer. Math. Soc. 83 (1956), 482–492.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Birkhäuser Verlag Basel
About this chapter
Cite this chapter
Benedetto, J.J., Heinig, H.P., Johnson, R. (1987). Fourier Inequalities With Ap-Weights. In: Walter, W. (eds) General Inequalities 5. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik Série internationale d’Analyse numérique, vol 80. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7192-1_17
Download citation
DOI: https://doi.org/10.1007/978-3-0348-7192-1_17
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-7194-5
Online ISBN: 978-3-0348-7192-1
eBook Packages: Springer Book Archive