The variation of the maximal function of a radial function

By Hannes Luiro. 2017

52 citations recorded by the source corpus.

We study the problem concerning the variation of the Hardy-Littlewood maximal function in higher dimensions. As the main result, we prove that the variation of the non-centered Hardy-Littlewood maximal function of a radial function is comparable to the variation of the function itself.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/cff9ba1639251dc1315c8bd8d92bf4384691ab43

Citations in the corpus

• Endpoint Sobolev and BV continuity for maximal operators, II (2017, unknown): “(fractional case) extending the main theorem in [CMP], however this proof does not work in the case β = 0. For some related results we refer to [BCHP], [CFS], [CaHu], [CaMo], [CaSv], [HM], [HO], [L], [L2] [LM], [Ma], [R] and [S]. 1.2. Discretesetting. Given a function f : Z→ R. We will keep the usua”