Weighted norm inequalities and homogeneous cones

Tatjana Ostrogorski

Colloquium Mathematicae (1998)

  • Volume: 77, Issue: 2, page 251-264
  • ISSN: 0010-1354

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Ostrogorski, Tatjana. "Weighted norm inequalities and homogeneous cones." Colloquium Mathematicae 77.2 (1998): 251-264. <http://eudml.org/doc/210588>.

@article{Ostrogorski1998,
author = {Ostrogorski, Tatjana},
journal = {Colloquium Mathematicae},
keywords = {homogeneous cone; power function; Hardy inequality; integral operator; homogeneous kernel; weight},
language = {eng},
number = {2},
pages = {251-264},
title = {Weighted norm inequalities and homogeneous cones},
url = {http://eudml.org/doc/210588},
volume = {77},
year = {1998},
}

TY - JOUR
AU - Ostrogorski, Tatjana
TI - Weighted norm inequalities and homogeneous cones
JO - Colloquium Mathematicae
PY - 1998
VL - 77
IS - 2
SP - 251
EP - 264
LA - eng
KW - homogeneous cone; power function; Hardy inequality; integral operator; homogeneous kernel; weight
UR - http://eudml.org/doc/210588
ER -

References

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  1. [1] W. Beckner, Inequalities in Fourier Analysis, Ann. of Math. 102 (1975), 159-182. Zbl0338.42017
  2. [2] A. Erdélyi, An extension of a Hardy-Littlewood-Pólya inequality, Proc. Edinburgh Math. Soc. 21 (1978), 11-15. Zbl0384.26009
  3. [3] J. Faraut and A. Koranyi, Analysis on Symmetric Cones, Oxford Univ. Press, Oxford, 1994. Zbl0841.43002
  4. [4] S. G. Gindikin, Analysis in homogeneous domains, Uspekhi Mat. Nauk 19 (1964), no. 4, 3-92 (in Russian). Zbl0144.08101
  5. [5] G. Hardy, J. Littlewood and G. Pólya, Inequalities, Cambridge Univ. Press, 1952. 
  6. [6] E. Hewitt and K. Ross, Abstract Harmonic Analysis, Vol. 1, Springer, 1963. Zbl0115.10603
  7. [7] M. Koecher, Positivitätsbereiche im n , Amer. J. Math. 79 (1957), 575-596. 
  8. [8] B. Muckenhoupt, Hardy's inequality with weights, Studia Math. 44 (1972), 31-38. Zbl0236.26015
  9. [9] T. Ostrogorski, Analogues of Hardy’s inequality in n , ibid. 88 (1988), 209-219. Zbl0639.42020
  10. [10] T. Ostrogorski, Homogeneous cones and Abelian theorems, Internat. J. Math. Math. Sci., to appear. Zbl0914.43008
  11. [11] O. Rothaus, Domains of positivity, Abh. Math. Sem. Univ. Hamburg 24 (1960), 189-235. Zbl0096.27903
  12. [12] Y. Sagher, M. V. Siadat and K. C. Zhou, Norm inequalities for integral operators on cones, Colloq. Math. 60/61 (1990), 77-92. Zbl0767.47014
  13. [13] M. V. Siadat and K. Zhou, An extension of norm inequalities for integral operators on cones when 0 p 1 , Proc. Amer. Math. Soc. 119 (1993), 817-821. Zbl0796.47019
  14. [14] E. B. Vinberg, The theory of homogeneous convex cones, Trudy Moskov. Mat. Obshch. 12 (1963), 303-358 (in Russian). 

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