On the regularity of one-sided fractional maximal functions

Year, pages: 2018, 1097 - 1112

In this paper we investigate the regularity properties of one-sided fractional maximal functions, both in continuous case and in discrete case. We prove that the one-sided fractional maximal operators $\mathcal{M}_β⁺$ and $\mathcal{M}_β^-$ map $W^1,p(\mathbb{R})$ into $W^1,q(\mathbb{R})$ with $1β⁺$ and $M_β^-$ from $\ell¹(\mathbb{Z})$ to ${ BV}(\mathbb{Z})$. Here ${ BV}(\mathbb{Z})$ denotes the set of all functions of bounded variation defined on $\mathbb{Z}$. The results we obtained represent significant and natural extensions of what was known previously.

Liu, F. 2018. On the regularity of one-sided fractional maximal functions. In Mathematica Slovaca, vol. 68, no.5, pp. 1097-1112. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0171

Liu, F. (2018). On the regularity of one-sided fractional maximal functions. Mathematica Slovaca, 68(5), 1097-1112. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0171