Weighted inequalities and the shape of approach regions

José García; Javier Soria

Studia Mathematica (1999)

  • Volume: 133, Issue: 3, page 261-274
  • ISSN: 0039-3223

Abstract

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We characterize geometric properties of a family of approach regions by means of analytic properties of the class of weights related to the boundedness of the maximal operator associated with this family.

How to cite

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García, José, and Soria, Javier. "Weighted inequalities and the shape of approach regions." Studia Mathematica 133.3 (1999): 261-274. <http://eudml.org/doc/216618>.

@article{García1999,
abstract = {We characterize geometric properties of a family of approach regions by means of analytic properties of the class of weights related to the boundedness of the maximal operator associated with this family.},
author = {García, José, Soria, Javier},
journal = {Studia Mathematica},
keywords = {approach regions; maximal operators; weights; weak-type estimates; shape; boundedness; homogeneous spaces},
language = {eng},
number = {3},
pages = {261-274},
title = {Weighted inequalities and the shape of approach regions},
url = {http://eudml.org/doc/216618},
volume = {133},
year = {1999},
}

TY - JOUR
AU - García, José
AU - Soria, Javier
TI - Weighted inequalities and the shape of approach regions
JO - Studia Mathematica
PY - 1999
VL - 133
IS - 3
SP - 261
EP - 274
AB - We characterize geometric properties of a family of approach regions by means of analytic properties of the class of weights related to the boundedness of the maximal operator associated with this family.
LA - eng
KW - approach regions; maximal operators; weights; weak-type estimates; shape; boundedness; homogeneous spaces
UR - http://eudml.org/doc/216618
ER -

References

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  1. [AC] M. Andersson and H. Carlsson, Boundary convergence in non-tangential and non-admissible approach regions, Math. Scand. 70 (1992), 293-301. Zbl0781.32010
  2. [CR] R. R. Coifman and R. Rochberg, Another characterization of BMO, Proc. Amer. Math. Soc. 79 (1980), 249-254. Zbl0432.42016
  3. [CW] R. R. Coifman et G. Weiss, Analyse Harmonique Non-Commutative sur Certains Espaces Homogènes, Lecture Notes in Math. 242, Springer, 1971. 
  4. [Ja] B. Jawerth, Weighted inequalities for maximal operators: linearization, localization and factorization, Amer. J. Math. 108 (1986), 361-414. Zbl0608.42012
  5. [NS] A. Nagel and E. M. Stein, On certain maximal functions and approach regions, Adv. Math. 54 (1984), 83-106. Zbl0546.42017
  6. [Pa] J. W. Pan, Weighted norm estimates for certain maximal operators with approach regions, in: Lecture Notes in Math. 1494, Springer, 1992, 169-175. 
  7. [SS1] A. Sánchez-Colomer and J. Soria, Weighted norm inequalities for general maximal operators and approach regions, Math. Nachr. 172 (1995), 249-260. Zbl0842.42009
  8. [SS2] A. Sánchez-Colomer and J. Soria, A p and approach regions, in: Fourier Analysis and Partial Differential Equations, CRC Press, 1995, 311-315. Zbl0871.42016
  9. [ST] J. O. Strömberg and A. Torchinsky, Weighted Hardy Spaces, Lecture Notes in Math. 1381, Springer, 1989. 
  10. [Su] J. Sueiro, On maximal functions and Poisson-Szegő integrals, Trans. Amer. Math. Soc. 298 (1986), 653-669. Zbl0612.32007

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