Abstract
In this paper we give some conditions on two weights for the maximal function M Ω to be of weak type (p,p). We also extend this result to the maximal functions of Poisson integrals.
Keywords
- Maximal Operator
- Maximal Function
- Approach Region
- Weak Type
- Homogeneous Type
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The Project Supported by National Natural Science Foundation of China
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References
A. P. Calderón, Inequalities for the maximal function relative to a metric, Studia Math. 57 (1976), 297–306.
R. R. Coifman and G. Weiss, Analyse harmonique non-commutative sur certain espaces homogenes, Lecture Notes in Math., Vol.242, Springer-Verlag, Berlin, 1971.
J.-L. Journé, Calderón-Zygmund operators pseudo-differential operators and the Cauchy integral of Calderón. Lect. Notes in Math. 994, Springer-Verlag, Berlin, 1983.
A. Nagel and E. M. Stein, On certain maximal functions and approach regions, Adv. in Math. 54 (1984), 83–106.
J. Sueiro, On maximal functions and Poisson-Szegö integrals, Tran. Amer. Math. Soc. Vol. 298, No.2 (1986), 653–669.
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© 1991 Springer-Verlag
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Pan, W. (1991). Weighted norm inequalities for certain maximal operators with approach regions. In: Cheng, MT., Deng, DG., Zhou, XW. (eds) Harmonic Analysis. Lecture Notes in Mathematics, vol 1494. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087768
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DOI: https://doi.org/10.1007/BFb0087768
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54901-7
Online ISBN: 978-3-540-46474-7
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