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

Studia Mathematica (1994)

- Volume: 110, Issue: 2, page 149-167
- ISSN: 0039-3223

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topBloom, S., and Kerman, R.. "Weighted Orlicz space integral inequalities for the Hardy-Littlewood maximal operator." Studia Mathematica 110.2 (1994): 149-167. <http://eudml.org/doc/216106>.

@article{Bloom1994,

abstract = {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.},

author = {Bloom, S., Kerman, R.},

journal = {Studia Mathematica},

keywords = {integral inequalities; Hardy-Littlewood maximal operator; weighted inequalities; Orlicz spaces},

language = {eng},

number = {2},

pages = {149-167},

title = {Weighted Orlicz space integral inequalities for the Hardy-Littlewood maximal operator},

url = {http://eudml.org/doc/216106},

volume = {110},

year = {1994},

}

TY - JOUR

AU - Bloom, S.

AU - Kerman, R.

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

JO - Studia Mathematica

PY - 1994

VL - 110

IS - 2

SP - 149

EP - 167

AB - 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.

LA - eng

KW - integral inequalities; Hardy-Littlewood maximal operator; weighted inequalities; Orlicz spaces

UR - http://eudml.org/doc/216106

ER -

## References

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- [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 ${L}_{\Phi}$ integral inequalities for operators of Hardy type, Studia Math. 110 (1994), 35-52. Zbl0823.42010
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- [6] A. S. Gogatishvili and L. Pick, Weighted inequalities of weak and extra-weak type for the maximal operator and Hilbert transform, preprint. Zbl0798.42009
- [7] R. Kerman and A. Torchinsky, Integral inequalities with weights for the Hardy maximal function, Studia Math. 71 (1981/82), 277-284. Zbl0517.42030
- [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. Zbl0095.09103
- [10] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226. Zbl0236.26016
- [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. Zbl0758.42012
- [13] M. M. Rao and Z. D. Ren, Theory of Orlicz Spaces, Marcel Dekker, New York, 1991. Zbl0724.46032
- [14] T. Shimogaki, Hardy-Littlewood majorants in function spaces, J. Math. Soc. Japan 17 (1965), 365-373. Zbl0135.16304
- [15] A. Zygmund, Trigonometric Series, Vol. I, 2nd ed., Cambridge Univ. Press, Cambridge, 1959. Zbl0085.05601

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