A note on maximal inequalities
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- by Wo Sang Young PDF
- Proc. Amer. Math. Soc. 36 (1972), 207-211 Request permission
Abstract:
D. L. Burkholder and S. Sawyer extended in two apparently different directions a theorem of E. M. Stein involving maximal inequalities as necessary conditions for almost everywhere convergence. We will unify these theorems by showing that the like conclusions follow from certain conditions which are implied by each of Burkholder’s and Sawyer’s hypotheses.References
- D. L. Burkholder, Maximal inequalities as necessary conditions for almost everywhere convergence, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 3 (1964), 75–88 (1964). MR 189110, DOI 10.1007/BF00531684
- S. Sawyer, Maximal inequalities of weak type, Ann. of Math. (2) 84 (1966), 157–174. MR 209867, DOI 10.2307/1970516
- E. M. Stein, On limits of seqences of operators, Ann. of Math. (2) 74 (1961), 140–170. MR 125392, DOI 10.2307/1970308
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 36 (1972), 207-211
- MSC: Primary 28A20
- DOI: https://doi.org/10.1090/S0002-9939-1972-0311866-0
- MathSciNet review: 0311866