Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772323 | Journal of Functional Analysis | 2017 | 33 Pages |
Abstract
In this paper we investigate some questions related to the continuity of maximal operators in W1,1 and BV spaces, complementing some well-known boundedness results. Letting MË be the one-dimensional uncentered Hardy-Littlewood maximal operator, we prove that the map fâ¦(MËf)â² is continuous from W1,1(R) to L1(R). In the discrete setting, we prove that MË:BV(Z)âBV(Z) is also continuous. For the one-dimensional fractional Hardy-Littlewood maximal operator, we prove by means of counterexamples that the corresponding continuity statements do not hold, both in the continuous and discrete settings, and for the centered and uncentered versions.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Emanuel Carneiro, José Madrid, Lillian B. Pierce,