# Littlewood-Paley theory on solenoids

Nakhlé Asmar; Stephen Montgomery-Smith

Colloquium Mathematicae (1993)

- Volume: 65, Issue: 1, page 69-82
- ISSN: 0010-1354

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top## How to cite

topAsmar, Nakhlé, and Montgomery-Smith, Stephen. "Littlewood-Paley theory on solenoids." Colloquium Mathematicae 65.1 (1993): 69-82. <http://eudml.org/doc/210207>.

@article{Asmar1993,

author = {Asmar, Nakhlé, Montgomery-Smith, Stephen},

journal = {Colloquium Mathematicae},

keywords = {Littlewood-Paley theory; solenoids; Stein's inequality},

language = {eng},

number = {1},

pages = {69-82},

title = {Littlewood-Paley theory on solenoids},

url = {http://eudml.org/doc/210207},

volume = {65},

year = {1993},

}

TY - JOUR

AU - Asmar, Nakhlé

AU - Montgomery-Smith, Stephen

TI - Littlewood-Paley theory on solenoids

JO - Colloquium Mathematicae

PY - 1993

VL - 65

IS - 1

SP - 69

EP - 82

LA - eng

KW - Littlewood-Paley theory; solenoids; Stein's inequality

UR - http://eudml.org/doc/210207

ER -

## References

top- [1] R. A. Beaumont and H. S. Zuckerman, A characterization of the subgroups of the additive rationals, Pacific J. Math. 1 (1951), 169-177. Zbl0043.02904
- [2] A. Benedek and R. Panzone, The spaces ${L}^{P}$, with mixed norms, Duke Math. J. 28 (1961), 301-324. Zbl0107.08902
- [3] C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, 1988. Zbl0647.46057
- [4] E. Berkson, T. A. Gillespie and P. S. Muhly, ${L}^{p}$-multiplier transference induced by representations in Hilbert space, Studia Math. 94 (1989), 51-61. Zbl0722.43001
- [5] D. L. Burkholder, B. J. Davis and R. F. Gundy, Integral inequalities for convex functions of operators on martingales, in: Proc. Sixth Berkeley Sympos. Math. Statist. Probab., Vol. 2, Univ. of California Press, Berkeley, Calif., 1972, 223-240. Zbl0253.60056
- [6] A. P. Calderòn, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113-190. Zbl0204.13703
- [7] J. Diestel and J. J. Uhl, Vector Measures, Math. Surveys 15, Amer. Math. Soc., Providence, R.I., 1977.
- [8] J. L. Doob, Stochastic Processes, Wiley Publications in Statistics, New York 1953.
- [9] R. E. Edwards and G. I. Gaudry, Littlewood-Paley and Multiplier Theory, Ergeb. Math. Grenzgeb. 90, Springer, Berlin 1977.
- [10] J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland, 1985.
- [11] A. M. Garsia, Martingale Inequalities, W. A. Benjamin, Reading, Mass., 1973.
- [12] E. Hewitt and G. Ritter, Fourier series on certain solenoids, Math. Ann. 257 (1981), 61-83. Zbl0448.42005
- [13] E. Hewitt and G. Ritter, Conjugate Fourier series on certain solenoids, Trans. Amer. Math. Soc. 273 (1983), 817-840. Zbl0521.43007
- [14] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. I, Springer, Berlin 1963. Zbl0115.10603
- [15] E. M. Stein, Topics in Harmonic Analysis Related to Littlewood-Paley Theory, Ann. of Math. Stud. 63, Princeton Univ. Press, 1985.

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