Geodesic
The Conjugate Function on the Finite Dimensional Torus
Canadian mathematical bulletin, Tome 32 (1989) no. 2, pp. 140-148

Voir la notice de l'article provenant de la source Cambridge University Press

We consider the group T a , its group of characters Z a , and an arbitrary order P on Z a . For x ∊ Z a , let sgnp x be 1, - 1 , or 0 according as x € P\{0}, x € (-P)\{0}, or X = 0. For f in Lp (T a ), 1 < p < ∞, it is known that there is a function in Lp (T a ) such that for all X in Z a . Summability methods for are also available. In this paper, we obtain summability methods for that apply for in L1 (T a ), and we show how various properties of can be derived from our construction.
DOI : 10.4153/CMB-1989-021-5
Mots-clés : 43A55 
Asmar, Nakhle. The Conjugate Function on the Finite Dimensional Torus. Canadian mathematical bulletin, Tome 32 (1989) no. 2, pp. 140-148. doi: 10.4153/CMB-1989-021-5
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[1] 1. Asmar, N. and Edwin Hewitt, Marcel Rieszs theorem on conjugate Fourier series and its descendants. Proceedings of the Analysis conference and workshop held in Singapore, 1986. Edited by T. L. Choy. North-Holland 1988. Google Scholar

[2] 2. Berkson, Earl and T.A. Gillespie, The generalized M. Riesz theorem and transference. Pacific J. Math. 120 (2) (1985), 279–288. Google Scholar

[3] 3. Calderon, Alberto P., Ergodic theory and translation-invariant operators. Proc. Nat. Aca. Sci. U.S.A., 59 (2) (1968), 855–857. Google Scholar

[4] 4. Helson, Henry, Conjugate series and a theorem of Paley. Pacific J. Math. 8 (1958), 437–446. Google Scholar

[5] 5. Hewitt, Edwin and Gunter Ritter, Conjugate Fourier series on certain solenoids. Trans. Amer. Math. Soc. 276 (2) (1983), 817–840. Google Scholar

[6] 6. Hewitt, Edwin and Kenneth Ross, Abstract harmonic analysis I. Grundlehren der mathematischen Wissenschaften, 115, Second Edition. Berlin, Heidelberg, New York: Springer-Verlag 1979. Google Scholar

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