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ArticleOriginal scientific text

Title

Some Sawyer type inequalities for martingales

Authors 1, 2

Affiliations

  1. Department of Mathematics, Kansas State University, Manhattan, Kansas 66506, U.S.A.
  2. Department of Mathematics, Brown University, Providence, Rhode Island 02912, U.S.A.

Abstract

Some martingale analogues of Sawyer's two-weight norm inequality for the Hardy-Littlewood maximal function Mf are shown for the Doob maximal function of martingales.

Bibliography

  1. J. L. Doob, Stochastic Processes, Wiley, New York, 1953.
  2. R. A. Hunt, D. S. Kurtz and C. J. Neugebauer, A note on the equivalence of Ap and Sawyer's condition for equal weights, in: Conf. Harmonic Analysis in Honor of A. Zygmund, Wadsworth, Belmont, Calif., 1981, 156-158.
  3. M. Izumisawa and N. Kazamaki, Weighted norm inequalities for martingales, Tôhoku Math. J. 29 (1977), 115-124.
  4. B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226.
  5. E. Sawyer, A characterization of a two weight norm inequality for maximal operators, Studia Math. 75 (1982), 1-11.
Studia Mathematica
1994/111/2
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Pages:
187-194
Main language of publication
English
Received
1993-11-02
Accepted
1994-03-02
Published
1994
Exact and natural sciences