Geometric Maximal Operators and BMO on Product Bases

Authors

Galia Dafni, Concordia University
Ryan Gibara, Université Laval
Hong Yue, Georgia College & State University

Document Type

Article

Publication Date

2020

Publication Title

Journal of Geometric Analysis

Abstract

We consider the problem of the boundedness of maximal operators on BMO on shapes in Rn. We prove that for bases of shapes with an engulfing property, the corresponding maximal function is bounded from BMO to BLO, generalising a known result of Bennett for the basis of cubes. When the basis of shapes does not possess an engulfing property but exhibits a product structure with respect to lower-dimensional shapes coming from bases that do possess an engulfing property, we show that the corresponding maximal function is bounded from BMO to a space we define and call rectangular BLO.

Department

Mathematics

Comments

© 2020, Mathematica Josephina, Inc.

DOI

10.1007/s12220-020-00501-3

Recommended Citation

Dafni, G., Gibara, R., & Yue, H. (2020). Geometric Maximal Operators and BMO on Product Bases. Journal of Geometric Analysis.