[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b180286

BOUNDEDNESS OF THE STRONG MAXIMAL OPERATOR WITH THE HAUSDORFF CONTENT

Saito, Hiroki (College of Science and Technology Nihon University)

Publication Information

Bulletin of the Korean Mathematical Society / v.56, no.2, 2019 , pp. 399-406 More about this Journal

Abstract

Let n be the spatial dimension. For d, $$0$ < $d{\leq}n$$ , let $H^d$ be the d-dimensional Hausdorff content. The purpose of this paper is to prove the boundedness of the dyadic strong maximal operator on the Choquet space $L^p(H^d,{\mathbb{R}}^n)$ for min(1, d) < p. We also show that our result is sharp.

Keywords

strong maximal operator; Hausdorff content;

Citations & Related Records

Reference

1	D. R. Adams, Choquet integrals in potential theory, Publ. Mat. 42 (1998), no. 1, 3-66. DOI
2	J. Orobitg and J. Verdera, Choquet integrals, Hausdorff content and the Hardy-Littlewood maximal operator, Bull. London Math. Soc. 30 (1998), no. 2, 145-150. DOI