A Note on the Regularity of the Two-Dimensional One-Sided Hardy-Littlewood Maximal Function. (5th August 2018) - Liu, Feng; Xu, Lei
Abstract : 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 spacesW s, p ( R 2 ) for0 ≤ s ≤ 1 and1 < p < ∞ . More importantly, we establish the sharp boundedness and continuity for the discrete two-dimensional one-sided Hardy-Littlewood maximal operator froml 1 ( Z 2 ) toB V ( Z 2 ) . HereB V ( Z 2 ) denotes the set of all functions of bounded variation onZ 2 .