A Note on the Boundedness of Doob Maximal Operators on a Filtered Measure Space
Let M be the Doob maximal operator on a filtered measure space and let v be an Ap weight with 1<p<+∞. We try proving that ∥Mf∥Lp(v)≤p′[v]Ap1p−1∥f∥Lp(v), where 1/p+1/p′=1. Although we do not find an approach which gives the constant p′, we obtain that ∥Mf∥Lp(v)≤p1p−1p′[v]Ap1p−1∥f∥Lp(v), with limp→+∞p1p−1=1.
2016 ◽
Vol 59
(3)
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pp. 533-547
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1989 ◽
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pp. 647-656
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2013 ◽
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pp. 920-946
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Vol 60
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pp. 586-603
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1998 ◽
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pp. 403-424
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