Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A Hardy-Littlewood maximal inequality for Jacobi type hypergroups

Authors: William C. Connett and Alan L. Schwartz
Journal: Proc. Amer. Math. Soc. 107 (1989), 137-143
MSC: Primary 43A10
MathSciNet review: 961411
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A Hardy-Littlewood maximal inequality is proved for a class of probability preserving measure algebras on compact intervals.

References [Enhancements On Off] (What's this?)

  • [1] R. Coifman and G. Weiss, Analyse harmonique non-commutative sur certains espaces homogenes, Lecture Notes in Mathematics, vol. 242, Springer-Verlag, Berlin and New York. MR 0499948 (58:17690)
  • [2] W. C. Connett and A. L. Schwartz, The theory of ultraspherical multipliers, Mem. Amer. Math. Soc., vol. 9, no. 183, 1977. MR 0435708 (55:8666)
  • [3] -, The Littlewood-Paley theory for Jacobi expansions, Trans. Amer. Math. Soc. 251 (1979), 219-234. MR 531976 (81g:42027)
  • [4] -, The harmonic machinery for eigenfunction expansions, Proc. Sympos. Pure Math., vol. 35, Amer. Math. Soc., Providence, R.I., pp. 429-434. MR 545335 (80k:33010)
  • [5] -, Analysis of a class of probability preserving measure algebras on a compact interval, Trans. Amer. Math. Soc. (to appear).
  • [6] G. H. Hardy and J. E. Littlewood, A maximal theorem with function theoretic applications, Acta Math. 54 (1930), 81-116. MR 1555303
  • [7] B. M. Levitan, Generalized translation operators, Israel Program for Scientific Translations, Jerusalem, 1964. MR 0172118 (30:2344)
  • [8] M. H. Protter and H. F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Englewood Cliffs, N.J., 1967. MR 0219861 (36:2935)
  • [9] E. M. Stein, Topics of harmonic analysis related to the Littlewood-Paley Theory, Ann. of Math. Stud., no. 63, Princeton Univ. Press, Princeton, N.J., 1970. MR 0252961 (40:6176)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 43A10

Retrieve articles in all journals with MSC: 43A10

Additional Information

Keywords: Measure algebra, maximal function, hypergroup
Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society