×

A Hardy-Littlewood maximal inequality for Jacobi type hypergroups. (English) Zbl 0691.43003

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

MSC:

43A10 Measure algebras on groups, semigroups, etc.
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ronald R. Coifman and Guido Weiss, Analyse harmonique non-commutative sur certains espaces homogènes, Lecture Notes in Mathematics, Vol. 242, Springer-Verlag, Berlin-New York, 1971 (French). Étude de certaines intégrales singulières. · Zbl 0224.43006
[2] W. C. Connett and A. L. Schwartz, The theory of ultraspherical multipliers, Mem. Amer. Math. Soc. 9 (1977), no. 183, iv+92. · Zbl 0367.42006 · doi:10.1090/memo/0183
[3] William C. Connett and Alan L. Schwartz, The Littlewood-Paley theory for Jacobi expansions, Trans. Amer. Math. Soc. 251 (1979), 219 – 234. · Zbl 0468.42010
[4] W. C. Connett and A. L. Schwartz, The harmonic machinery for eigenfunction expansions, Harmonic analysis in Euclidean spaces (Proc. Sympos. Pure Math., Williams Coll., Williamstown, Mass., 1978) Proc. Sympos. Pure Math., XXXV, Part, Amer. Math. Soc., Providence, R.I., 1979, pp. 429 – 434. · Zbl 0418.42008
[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), no. 1, 81 – 116. · JFM 56.0264.02 · doi:10.1007/BF02547518
[7] B. M. Levitan, Generalized translation operators and some of their applications, Translated by Z. Lerman; edited by Don Goelman, Israel Program for Scientific Translations, Jerusalem; Daniel Davey & Co., Inc., 1964. · Zbl 0192.48902
[8] Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. · Zbl 0549.35002
[9] Elias M. Stein, Topics in harmonic analysis related to the Littlewood-Paley theory., Annals of Mathematics Studies, No. 63, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1970. · Zbl 0193.10502
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.