Hostname: page-component-5b777bbd6c-f9nfp Total loading time: 0 Render date: 2025-06-24T20:31:33.339Z Has data issue: false hasContentIssue false
  • English
  • Français

The Hilbert Transform on Rearrangement-Invariant Spaces

Published online by Cambridge University Press:  20 November 2018

D. W. Boyd
D. W. Boyd*
Affiliation:
University of Toronto
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The purpose of this paper is to investigate conditions under which the Hilbert transform defines a bounded linear operator from a given function space into itself. The spaces with which we deal have the property of rearrangement-invariance which is defined in §1. This class of spaces includes the Lebesgue, Orlicz, and Lorentz spaces.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 599 - 616
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Boyd, D. W., The Hilbert Transformation on rearrangement invariant function spaces, Thesis, University of Toronto (1966).Google Scholar
2. Calderón, A. P., Intermediate spaces and interpolation, the complex method, Studia Math., 24 (1964), 113–190.Google Scholar
3. Halperin, I., Uniform convexity in function spaces, Duke Math. J., 21 (1954), 195–204.Google Scholar
4. Halperin, I., Reflexivity in the Lλ function spaces, Duke Math. J., 21 (1954), 205–208.Google Scholar
5. Hardy, G. H., Littlewood, J. E., and Polyá, G., Inequalities (Cambridge, 1934).Google Scholar
6. Hille, E. and Phillips, R. S., Functional analysis and semi-groups (Providence, 1957).Google Scholar
7. Lorentz, G. G., Some new functional spaces, Ann. Math., (2), 51 (1950), 27–55.Google Scholar
8. Lorentz, G. G., Bernstein polynomials (Toronto, 1953).Google Scholar
9. Luxemburg, W. A. J., Banach function spaces, Thesis, Delft Technical Univ. (1955).Google Scholar
10. O'Neil, R. and Weiss, G., The Hilbert transform and rearrangement of functions, Studia Math., 23 (1963), 189–198.Google Scholar
11. Ryan, R., Conjugate functions in Orlicz spaces, Pacific J. Math., 13 (1963), 1371–1377.Google Scholar