A Hardy-Littlewood maximal inequality for Jacobi type hypergroups

A Hardy-Littlewood maximal inequality for Jacobi type hypergroups
HTML articles powered by AMS MathViewer

Proc. Amer. Math. Soc. 107 (1989), 137-143

DOI: https://doi.org/10.1090/S0002-9939-1989-0961411-4

PDF | Request permission

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

References

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. MR 0499948
W. C. Connett and A. L. Schwartz, The theory of ultraspherical multipliers, Mem. Amer. Math. Soc. 9 (1977), no. 183, iv+92. MR 435708, DOI 10.1090/memo/0183
William C. Connett and Alan L. Schwartz, The Littlewood-Paley theory for Jacobi expansions, Trans. Amer. Math. Soc. 251 (1979), 219–234. MR 531976, DOI 10.1090/S0002-9947-1979-0531976-3
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. MR 545335

Analysis of a class of probability preserving measure algebras on a compact interval

G. H. Hardy and J. E. Littlewood, A maximal theorem with function-theoretic applications, Acta Math. 54 (1930), no. 1, 81–116. MR 1555303, DOI 10.1007/BF02547518
B. M. Levitan, Generalized translation operators and some of their applications, Israel Program for Scientific Translations, Jerusalem; Daniel Davey & Co., Inc., 1964. Translated by Z. Lerman; edited by Don Goelman. MR 0172118
Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0219861
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. MR 0252961