The size of ( L 2 , L p ) multipliers

Kathryn Hare

Colloquium Mathematicae (1992)

  • Volume: 63, Issue: 2, page 249-262
  • ISSN: 0010-1354

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Hare, Kathryn. "The size of $(L^2,L^p)$ multipliers." Colloquium Mathematicae 63.2 (1992): 249-262. <http://eudml.org/doc/210150>.

@article{Hare1992,
author = {Hare, Kathryn},
journal = {Colloquium Mathematicae},
keywords = {compact abelian group; Fourier transform; multiplier; -improving multipliers; Riesz products; sums of dissociate sets},
language = {eng},
number = {2},
pages = {249-262},
title = {The size of $(L^2,L^p)$ multipliers},
url = {http://eudml.org/doc/210150},
volume = {63},
year = {1992},
}

TY - JOUR
AU - Hare, Kathryn
TI - The size of $(L^2,L^p)$ multipliers
JO - Colloquium Mathematicae
PY - 1992
VL - 63
IS - 2
SP - 249
EP - 262
LA - eng
KW - compact abelian group; Fourier transform; multiplier; -improving multipliers; Riesz products; sums of dissociate sets
UR - http://eudml.org/doc/210150
ER -

References

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  1. [1] H. Beckner, S. Janson and J. Jerison, Convolution inequalities on the circle, in: Conference on Harmonic Analysis in Honor of Antoni Zygmund (W. Beckner et al., eds.), Wadsworth, Belmont 1983, 32-43. 
  2. [2] A. Bonami, Étude des coefficients de Fourier des fonctions de L p ( G ) , Ann. Inst. Fourier (Grenoble) 20 (2) (1970), 335-402. Zbl0195.42501
  3. [3] M. Christ, A convolution inequality concerning Cantor-Lebesgue measures, Rev. Mat. Iberoamericana 1 (1985), 75-83. Zbl0644.42011
  4. [4] R. E. Edwards, Fourier Series, Vol. 2, Springer, New York 1982. Zbl0599.42001
  5. [5] C. Graham, K. Hare and D. Ritter, The size of L p -improving measures, J. Funct. Anal. 84 (1989), 472-495. Zbl0678.43001
  6. [6] C. C. Graham and O. C. McGehee, Essays in Commutative Harmonic Analysis, Springer, New York 1979. Zbl0439.43001
  7. [7] K. Hare, A characterization of L p -improving measures, Proc. Amer. Math. Soc. 102 (1988), 295-299. Zbl0664.43001
  8. [8] K. Hare, Properties and examples of ( L p , L q ) multipliers, Indiana Univ. Math. J. 38 (1989), 211-227. Zbl0655.43003
  9. [9] R. Larson, An Introduction to the Theory of Multipliers, Grundlehren Math. Wiss. 175, Springer, New York, 1971. 
  10. [10] J. López and K. Ross, Sidon Sets, Lecture Notes in Pure Appl. Math. 13, Marcel Dekker, New York 1975. 
  11. [11] D. Oberlin, A convolution property of the Cantor-Lebesgue measure, Colloq. Math. 67 (1982), 113-117. Zbl0501.42007
  12. [12] J. Price, Some strict inclusions between spaces of L p -multipliers, Trans. Amer. Math. Soc. 152 (1970), 321-330. Zbl0216.14802
  13. [13] D. Ritter, Most Riesz product mesures are L p -improving, Proc. Amer. Math. Soc. 97 (1986), 291-295. Zbl0593.43002
  14. [14] D. Ritter, Some singular measures on the circle which improve L p spaces, Colloq. Math. 52 (1987), 133-144. Zbl0637.43002
  15. [15] W. Rudin, Trigonometric series with gaps, J. Math. Mech. 9 (1960), 203-227. Zbl0091.05802
  16. [16] E. M. Stein, Harmonic analysis on R n , in: Studies in Harmonic Analysis, MAA Stud. Math. 13, J. M. Ash (ed.), 1976, 97-135. 

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