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1994 | 110 | 2 | 149-167
Tytuł artykułu

Weighted Orlicz space integral inequalities for the Hardy-Littlewood maximal operator

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Necessary and sufficient conditions are given for the Hardy-Littlewood maximal operator to be bounded on a weighted Orlicz space when the complementary Young function satisfies $Δ_2$. Such a growth condition is shown to be necessary for any weighted integral inequality to occur. Weak-type conditions are also investigated.
Słowa kluczowe
Czasopismo
Rocznik
Tom
110
Numer
2
Strony
149-167
Opis fizyczny
Daty
wydano
1994
otrzymano
1993-06-23
poprawiono
1993-11-05
Twórcy
autor
  • Department of Mathematics, Siena College, Loudonville, New York 12211, U.S.A.
autor
  • Department of Mathematics, Brock University, St. Catharines, Ontario LS2A1, Canada
Bibliografia
  • [1] R. Bagby, Weak bounds for the maximal function in weighted Orlicz spaces, Studia Math. 95 (1990), 195-204.
  • [2] N. K. Bari and S. B. Stečkin [S. B. Stechkin], Best approximation and differential properties of two conjugate functions, Trudy Moskov. Mat. Obshch. 5 (1956), 483-522 (in Russian).
  • [3] S. Bloom and R. Kerman, Weighted $L_Φ$ integral inequalities for operators of Hardy type, Studia Math. 110 (1994), 35-52.
  • [4] R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241-250.
  • [5] A. S. Gogatishvili, General weak-type estimates for the maximal operators and singular integrals, preprint.
  • [6] A. S. Gogatishvili and L. Pick, Weighted inequalities of weak and extra-weak type for the maximal operator and Hilbert transform, preprint.
  • [7] R. Kerman and A. Torchinsky, Integral inequalities with weights for the Hardy maximal function, Studia Math. 71 (1981/82), 277-284.
  • [8] V. Kokilashvili and M. Krbec, Weighted Inequalities in Lorentz and Orlicz Spaces, World Scientific, 1991.
  • [9] M. A. Krasnosel'skii [M. A. Krasnosel'skiǐ] and Ya. B. Rutickii [Ya. B. Rutitskiǐ], Convex Functions and Orlicz Spaces, Noordhoff, Groningen, 1961.
  • [10] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226.
  • [11] L. Pick, Weighted inequalities for the Hardy-Littlewood maximal operators in Orlicz spaces, preprint.
  • [12] L. Quinsheng, Two weight Φ-inequalities for the Hardy operator, Hardy-Littlewood maximal operator and fractional integrals, Proc. Amer. Math. Soc., to appear.
  • [13] M. M. Rao and Z. D. Ren, Theory of Orlicz Spaces, Marcel Dekker, New York, 1991.
  • [14] T. Shimogaki, Hardy-Littlewood majorants in function spaces, J. Math. Soc. Japan 17 (1965), 365-373.
  • [15] A. Zygmund, Trigonometric Series, Vol. I, 2nd ed., Cambridge Univ. Press, Cambridge, 1959.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv110i2p149bwm
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