A Note on the Regularity of the Two-Dimensional One-Sided Hardy-Littlewood Maximal Function

Abstract EN

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

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.