Reverse-Holder classes in the Orlicz spaces setting

• Autorzy: E. Harboure , O. Salinas , B. Viviani
• Języki publikacji: EN

Abstrakty

EN

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 $⋂_{q>1}RH_q$.

Słowa kluczowe

EN

reverse-Hölder class; $A_p$ classes of Muckenhoupt; Orlicz spaces

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 130
• Numer: 3
• Strony: 245-261

Daty

wydano

1998

otrzymano

1997-09-16

poprawiono

1998-01-12

Twórcy

autor

E. Harboure

• Programa Especial de Matemática Aplicada, Universidad Nacional del Litoral, Güemes 3450, 3000 Santa Fe, República Argentina

autor

O. Salinas

• Programa Especial de Matemática Aplicada, Universidad Nacional del Litoral, Güemes 3450, 3000 Santa Fe, República Argentina

autor

B. Viviani

• Programa Especial de Matemática Aplicada, Universidad Nacional del Litoral, Güemes 3450, 3000 Santa Fe, República Argentina

Bibliografia

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