Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 453-472

THE LOCAL SHARP MAXIMAL FUNCTION AND BMO ON LOCALLY HOMOGENEOUS SPACES

Marco Bramanti and Maria Stella Fanciullo

Politecnico di Milano, Dipartimento di Matematica
Via Bonardi 9, 20133 Milano, Italy; marco.bramanti 'at' polimi.it

Università di Catania, Dipartimento di Matematica e Informatica
Viale Andrea Doria 6, 95125 Catania, Italy; fanciullo 'at' dmi.unict.it

Abstract. We prove a local version of Fefferman–Stein inequality for the local sharp maximal function, and a local version of John–Nirenberg inequality for locally BMO functions, in the framework of locally homogeneous spaces, in the sense of Bramanti–Zhu [3].

2010 Mathematics Subject Classification: Primary 42B25; Secondary 42B35, 46E30.

Key words: Locally homogeneous space, local sharp maximal function, local BMO, Fefferman–Stein inequality, John–Nirenberg inequality.

Reference to this article: M. Bramanti and M. S. Fanciullo: The local sharp maximal function and BMO on locally homogeneous spaces. Ann. Acad. Sci. Fenn. Math. 42 (2017), 453-472.

Full document as PDF file

https://doi.org/10.5186/aasfm.2017.4229