Reverse-Holder classes in the Orlicz spaces setting

E. Harboure; O. Salinas; B. Viviani

Studia Mathematica (1998)

  • Volume: 130, Issue: 3, page 245-261
  • ISSN: 0039-3223

Abstract

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In connection with the A ϕ classes of weights (see [K-T] and [B-K]), we study, in the context of Orlicz spaces, the corresponding reverse-Hölder classes R H ϕ . We prove that when ϕ is Δ 2 and has lower index greater than one, the class R H ϕ coincides with some reverse-Hölder class R H q , q > 1 . For more general ϕ we still get R H ϕ ⊂ A ∞ = ⋃ q > 1 R H q although the intersection of all these R H ϕ gives a proper subset of ⋂ q > 1 R H q .

How to cite

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Harboure, E., Salinas, O., and Viviani, B.. "Reverse-Holder classes in the Orlicz spaces setting." Studia Mathematica 130.3 (1998): 245-261. <http://eudml.org/doc/216556>.

@article{Harboure1998,
abstract = {In connection with the $A_ϕ $ classes of weights (see [K-T] and [B-K]), we study, in the context of Orlicz spaces, the corresponding reverse-Hölder classes $RH_ϕ$. We prove that when ϕ is $Δ_2$ and has lower index greater than one, the class $RH_ϕ$ coincides with some reverse-Hölder class $RH_q,q>1$. For more general ϕ we still get $RH_ϕ ⊂ A_∞ = ⋃_\{q>1\}RH_q$ although the intersection of all these $RH_ϕ$ gives a proper subset of $⋂_\{q>1\}RH_q$.},
author = {Harboure, E., Salinas, O., Viviani, B.},
journal = {Studia Mathematica},
keywords = {reverse-Hölder class; $A_p$ classes of Muckenhoupt; Orlicz spaces; class of Muckenhoupt; Orlicz space},
language = {eng},
number = {3},
pages = {245-261},
title = {Reverse-Holder classes in the Orlicz spaces setting},
url = {http://eudml.org/doc/216556},
volume = {130},
year = {1998},
}

TY - JOUR
AU - Harboure, E.
AU - Salinas, O.
AU - Viviani, B.
TI - Reverse-Holder classes in the Orlicz spaces setting
JO - Studia Mathematica
PY - 1998
VL - 130
IS - 3
SP - 245
EP - 261
AB - In connection with the $A_ϕ $ classes of weights (see [K-T] and [B-K]), we study, in the context of Orlicz spaces, the corresponding reverse-Hölder classes $RH_ϕ$. We prove that when ϕ is $Δ_2$ and has lower index greater than one, the class $RH_ϕ$ coincides with some reverse-Hölder class $RH_q,q>1$. For more general ϕ we still get $RH_ϕ ⊂ A_∞ = ⋃_{q>1}RH_q$ although the intersection of all these $RH_ϕ$ gives a proper subset of $⋂_{q>1}RH_q$.
LA - eng
KW - reverse-Hölder class; $A_p$ classes of Muckenhoupt; Orlicz spaces; class of Muckenhoupt; Orlicz space
UR - http://eudml.org/doc/216556
ER -

References

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  1. [B-K] S. Bloom and R. Kerman, Weighted Orlicz space integral inequalities for the Hardy-Littlewood maximal operator, Studia Math. 110 (1994), 149-167. Zbl0813.42014
  2. [CU-N] D. Cruz-Uribe, and C. J. Neugebauer, The structure of the reverse-Hölder classes, Trans. Amer. Math. Soc. 345 (1995), 2941-2960. Zbl0851.42016
  3. [C-F] R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241-250. Zbl0291.44007
  4. [F] B. Franchi, Weighted Sobolev-Poincaré inequalities and pointwise estimates for a class of degenerate elliptic equations, Trans. Amer. Math. Soc. 327 (1991), 125-158. Zbl0751.46023
  5. [K-K] V. Kokilashvili and M. Krbec, Weighted Inequalities in Lorentz and Orlicz Spaces, World Sci., Singapore, 1991. Zbl0751.46021
  6. [K-T] R. Kerman and A. Torchinsky, Integral inequalities with weights for the Hardy maximal function, Studia Math. 71 (1982), 278-284. Zbl0517.42030
  7. [S-T] J. Strömberg and A. Torchinsky, Weighted Hardy Spaces, Lecture Notes in Math. 1281, Springer, 1989. 

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