# 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

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topHarboure, 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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- [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
- [C-F] R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241-250. Zbl0291.44007
- [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
- [K-K] V. Kokilashvili and M. Krbec, Weighted Inequalities in Lorentz and Orlicz Spaces, World Sci., Singapore, 1991. Zbl0751.46021
- [K-T] R. Kerman and A. Torchinsky, Integral inequalities with weights for the Hardy maximal function, Studia Math. 71 (1982), 278-284. Zbl0517.42030
- [S-T] J. Strömberg and A. Torchinsky, Weighted Hardy Spaces, Lecture Notes in Math. 1281, Springer, 1989.

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