A General Approach to Littlewood-Paley Theorems for Orthogonal Families
Canadian mathematical bulletin, Tome 40 (1997) no. 3, pp. 296-308

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

A general lacunary Littlewood-Paley type theorem is proved, which applies in a variety of settings including Jacobi polynomials in [0, 1], SU(2), and the usual classical trigonometric series in [0, 2π). The theoremis used to derive new results for Lp multipliers on SU(2) and Jacobi Lp multipliers.
DOI : 10.4153/CMB-1997-036-1
Mots-clés : Primary: 42B25, secondary: 42C10, 43A80, Littlewood-Paley theorem, orthogonal decompositions, multipliers
Hare, Kathryn E. A General Approach to Littlewood-Paley Theorems for Orthogonal Families. Canadian mathematical bulletin, Tome 40 (1997) no. 3, pp. 296-308. doi: 10.4153/CMB-1997-036-1
@article{10_4153_CMB_1997_036_1,
     author = {Hare, Kathryn E.},
     title = {A {General} {Approach} to {Littlewood-Paley} {Theorems} for {Orthogonal} {Families}},
     journal = {Canadian mathematical bulletin},
     pages = {296--308},
     year = {1997},
     volume = {40},
     number = {3},
     doi = {10.4153/CMB-1997-036-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1997-036-1/}
}
TY  - JOUR
AU  - Hare, Kathryn E.
TI  - A General Approach to Littlewood-Paley Theorems for Orthogonal Families
JO  - Canadian mathematical bulletin
PY  - 1997
SP  - 296
EP  - 308
VL  - 40
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1997-036-1/
DO  - 10.4153/CMB-1997-036-1
ID  - 10_4153_CMB_1997_036_1
ER  - 
%0 Journal Article
%A Hare, Kathryn E.
%T A General Approach to Littlewood-Paley Theorems for Orthogonal Families
%J Canadian mathematical bulletin
%D 1997
%P 296-308
%V 40
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1997-036-1/
%R 10.4153/CMB-1997-036-1
%F 10_4153_CMB_1997_036_1

[1] 1. Askey, R., A transplantation theorem for Jacobi series, Illinois J. Math. 13 (1969), 583–590. Google Scholar

[2] 2. Askey, R. and Hirschman, I., Mean summability for ultraspherical polynomials, Math. Scand. 12 (1963), 167–177. Google Scholar

[3] 3. Bavinck, H., A special class of Jacobi series and applications, J. Math. Anal. Appl. 37 (1972), 767–797. Google Scholar

[4] 4. Bonami, A. and Clerc, J.-L., Sommes de Cesaro et multiplicateurs des developpements en harmoniques spheriques, Trans. Amer.Math. Soc. 183 (1973), 223–263. Google Scholar

[5] 5. Clerc, J.-L., Sommes de Riesz et multiplicateurs sur un groupe de Lie compact, Ann. Inst. Fourier (Grenoble) 24 (1974), 149–172. Google Scholar

[6] 6. Coifman, R. and Weiss, G., Central multiplier theorems for compact Lie groups, Bull. Amer. Math. Soc. 80 (1974), 124–126. Google Scholar

[7] 7. Connett, W. and Schwartz, A., The theory of ultraspherical multipliers, Mem. Amer. Math. Soc. (183) 9 (1977). Google Scholar

[8] 8. Connett, W. and Schwartz, A., A multiplier theorem for Jacobi expansions, Studia Math. 52 (1975), 243–261. Google Scholar

[9] 9. Connett, W. and Schwartz, A., The Littlewood-Paley theory for Jacobi expansions, Trans.Amer.Math. Soc. 251 (1979), 219–234. Google Scholar

[10] 10. Edwards, R. and Gaudry, G., Littlewood-Paley and multiplier theory, Springer-Verlag, Berlin, Heidelberg, 1977. Google Scholar

[11] 11. Gaudry, G., Littlewood-Paley theorems for sum and difference sets, Math. Proc. Cambridge Philos. Soc. 83 (1978), 65–71. Google Scholar

[12] 12. Hare, K., Lp-improving measures on compact non-abelian groups, J. Austral. Math. Soc. 46 (1989), 402–414. Google Scholar

[13] 13. Hare, K., Properties and examples of (Lp, Lq) multipliers, Indiana Univ. Math. J. 38 (1989), 211–227. Google Scholar

[14] 14. Hare, K. and Klemes, I., A new type of Littlewood-Paley partition, Ark.Mat. 30 (1992), 297–309. Google Scholar

[15] 15. Hare, K. and Klemes, I., On permutations of lacunary intervals, Trans. Amer. Math. Soc. 347 (1995), 4105–4127. Google Scholar

[16] 16. Hewitt, E. and Ross, K., Abstract harmonic analysis, Vol.II, Springer-Verlag, Berlin, Heidelberg, New York, 1979. Google Scholar

[17] 17. Inglis, I., Central multipliers which vanish at infinity, J. London Math. Soc. 19 (1979), 102–106. Google Scholar

[18] 18. Muckenhoupt, B. and Stein, E., Classical expansions and their relation to conjugate harmonic functions, Trans. Amer. Math. Soc. 118 (1965), 17–92. Google Scholar

[19] 19. Pollard, H., The mean convergence of orthogonal series. II,Trans. Amer.Math. Soc. 63 (1948), 355–367. Google Scholar

[20] 20. Price, J., Non ci sono insiemi infiniti di tipo Λ(p) per SU(2), Boll. Un. Mat. Ital. 4 (1971), 879–881. Google Scholar

[21] 21. Rubio de Francia, J., A Littlewood-Paley inequality for arbitrary intervals, Rev.Mat. Iberoamericana (2) 1 (1985), 1–14. Google Scholar

[22] 22. Sjogren, P. and Sjolin, P., Littlewood-Paley decompositions and Fourier multipliers with singularities on certain sets, Ann. Inst. Fourier (Grenoble) 31 (1981), 157–175. Google Scholar

[23] 23. Stein, E. and Weiss, G., Introduction to Fourier analysis on Euclidean spaces, Princeton Univ. Press, New Jersey, 1971. Google Scholar

[24] 24. Strichartz, R., Multipliers for spherical harmonic expansions, Trans. Amer.Math. Soc. 167 (1972), 115–124. Google Scholar

[25] 25. Szego, G., Orthogonal polynomials, Amer.Math. Soc. 23, New York, 1975. Google Scholar

[26] 26. Weiss, N., Lp estimates for bi-invariant operators on compact Lie groups, Amer. J. Math. 94 (1972), 103–118. Google Scholar

Cité par Sources :