Geodesic
The John–Nirenberg type inequality for non-doubling measures
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
Studia Mathematica, Tome 181 (2007) no. 2, pp. 153-170 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm181-2-3
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

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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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

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