A Note on the Regularity of the Two-Dimensional One-Sided Hardy-Littlewood Maximal Function
Keyword(s):
We investigate the regularity properties of the two-dimensional one-sided Hardy-Littlewood maximal operator. We point out that the above operator is bounded and continuous on the Sobolev spaces Ws,p(R2) for 0≤s≤1 and 1<p<∞. More importantly, we establish the sharp boundedness and continuity for the discrete two-dimensional one-sided Hardy-Littlewood maximal operator from l1(Z2) to BV(Z2). Here BV(Z2) denotes the set of all functions of bounded variation on Z2.
2011 ◽
Vol 363
(04)
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pp. 1699-1699
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Keyword(s):
2017 ◽
Vol 60
(3)
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pp. 586-603
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2015 ◽
Vol 58
(4)
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pp. 808-817
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Keyword(s):
1994 ◽
Vol 46
(5)
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pp. 1057-1072
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