Hostname: page-component-54dcc4c588-mz6gc Total loading time: 0 Render date: 2025-09-14T16:23:06.928Z Has data issue: false hasContentIssue false
  • English
  • Français

About the # Function

Published online by Cambridge University Press:  20 November 2018

G. T. Klincsek
G. T. Klincsek*
Affiliation:
Dept. of Maths., McGill University Montreal, Quebec, Canada H3C 3G1
Rights & Permissions [Opens in a new window]

Abstract

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 use of decreasing rearrangement formulas, and particularly that of the weak N inequality, is illustrated by deriving from E τ |f-f(τ -)|≤E τ u (where f t is some stochastic process and τ arbitrary stopping time) the estimate ||f||≤Const||u|| in the class of structureless norms with finite dual Hardy bound.

The basic estimate is

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 4 , 01 December 1976 , pp. 455 - 460
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Boyd, D. W., Indices of function spaces and their relationship to interpolation, Canadian Journ. Math. 21 (1969) pp. 1245–1254.Google Scholar
2. Fefferman, C. and Stein, E. M., Hp spaces of several variables, Acta Math. 129 (1972), pp. 137–193.Google Scholar
3. Garsia, A. M., Martingale Inequalities, W. A. Benjamin Inc., Reading, Mass. 1973.Google Scholar
4. Herz, C., A best possible Marcinkiewicz interpolation theorem with applications to martingale inequalities, McGill University, Dept. of Mathematics, lecture notes.Google Scholar
5. Herz, C., Cadlag processes, McGill University, Dept. of Mathematics, lecture notes.Google Scholar
6. John, F. and Nirenberg, L., On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), pp. 415–426.Google Scholar
7. Klincsek, G. T., Banach spaces of martingales in connection with Hp-spaces, Ph.D. thesis, McGill University.Google Scholar
8. Luxemburg, W. A. J., Rearrangement-invariant Banach function spaces, Queen’s papers in Pure & Applied Math. 10 (1967), pp. 83–144.Google Scholar
9. Meyer, P. A., Martingales and Stochastic Integrals I. Springer Lecture Notes in Math. 284 (1972).Google Scholar