1Department of Mathematics and Information Sciences Tokyo Metropolitan University Minami-Ohsawa 1-1, Hachioji-shi Tokyo 192-0397, Japan 2Graduate School of Mathematical Sciences The University of Tokyo 3-8-1 Komaba, Meguro-ku Tokyo 153-8914, Japan
Studia Mathematica, Tome 181 (2007) no. 2, pp. 153-170
X. Tolsa defined a space of BMO type
for positive Radon measures
satisfying some growth condition on $\mathbb R^d$.
This new BMO space is very suitable
for the Calderón–Zygmund theory
with non-doubling measures.
Especially,
the John–Nirenberg type inequality can be recovered.
In the present paper
we introduce a localized and weighted version of this inequality
and, as applications,
we obtain
some vector-valued inequalities and weighted inequalities
for Morrey spaces.
Keywords:
tolsa defined space bmo type positive radon measures satisfying growth condition mathbb bmo space suitable calder zygmund theory non doubling measures especially john nirenberg type inequality recovered present paper introduce localized weighted version inequality applications obtain vector valued inequalities weighted inequalities morrey spaces
Affiliations des auteurs :
Yoshihiro Sawano
1
;
Hitoshi Tanaka
2
1
Department of Mathematics and Information Sciences Tokyo Metropolitan University Minami-Ohsawa 1-1, Hachioji-shi Tokyo 192-0397, Japan
2
Graduate School of Mathematical Sciences The University of Tokyo 3-8-1 Komaba, Meguro-ku Tokyo 153-8914, Japan
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title = {The {John{\textendash}Nirenberg} type inequality for non-doubling measures},
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Yoshihiro Sawano; Hitoshi Tanaka. The John–Nirenberg type inequality for non-doubling measures. Studia Mathematica, Tome 181 (2007) no. 2, pp. 153-170. doi: 10.4064/sm181-2-3
