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

作者：Liu, Feng^*; Xu, Lei

来源：Journal of Function Spaces, 2018, 2018: 6759632.

DOI：10.1155/2018/6759632

• END-POINT REGULARITY
• BOUNDEDNESS
• EXISTENCE
• OPERATOR

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 W-s,W-p(R-2) for 0 <= s < 1 and 1 <= p < infinity. More importantly, we establish the sharp boundedness and continuity for the discrete two-dimensional one-sided Hardy-Littlewood maximal operator from l(1)(Z(2)) to BV(Z(2)). Here BV(Z(2)) denotes the set of all functions of bounded variation on Z(2).

• 出版日期2018
• 单位山东科技大学