On a maximal function related to Muckenhoupt's condition (in Russian) |
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| Author |
I.I. Mechnikov Odesa National University
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| Abstract |
We introduce the maximal function which is connected with the Muckenhoupt $A_1$ condition. The estimate for the equimeasurable rearrangement is obtained in terms of this maximal function. In particular, this estimate allows us to obtain the well-known Muckenhoupt lemma. The connection between boundedness of such maximal function and continuity of the initial function is investigated as well.
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| Keywords |
maximal function, Muckenhoupt condition, equimeasurable condition
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| DOI |
doi:10.30970/ms.23.2.143-148
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Reference |
1. Muckenhoupt B. Weighted norm inequalities for the Hardy maximal function// Trans. Amer. Math. Soc. -- 1972. -- V. 165. -- P. 207--226.
2. Mateu J., Mattila P., Nicolau A., Orobitg J. $BMO$ for nondoubling measure // Duke Math. J. -- 2000. -- V. 102, no. 3. -- P. 533--565. 3. Spanne S. Some function spaces defined using the mean oscillation over cube // Ann. Sc. norm. super. Pisa. -- 1965. -- V. 19, no. 4. -- P. 593--608. |
| Pages |
143-148
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| Volume |
23
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| Issue |
2
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| Year |
2005
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| Journal |
Matematychni Studii
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