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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## The Campanato, Morrey and Hölder spaces on spaces of homogeneous type

### Tom 176 / 2006

Studia Mathematica 176 (2006), 1-19 MSC: Primary 46E35; Secondary 46E30, 46E15, 42B35. DOI: 10.4064/sm176-1-1

#### Streszczenie

We investigate the relations between the Campanato, Morrey and Hölder spaces on spaces of homogeneous type and extend the results of Campanato, Mayers, and Macías and Segovia. The results are new even for the $\mathbb R^n$ case. Let $(X,d,\mu)$ be a space of homogeneous type and $(X,\delta,\mu)$ its normalized space in the sense of Macías and Segovia. We also study the relations of these function spaces for $(X,d,\mu)$ and for $(X,\delta,\mu)$. Using these relations, we can show that theorems for the Campanato, Morrey or Hölder spaces on the normal space are valid for the function spaces on any space of homogeneous type. As an application we obtain boundedness of some operators related to partial differential equations, boundedness of fractional differential and integral operators, and give characterizations of pointwise multipliers.

#### Autorzy

• Eiichi NakaiDepartment of Mathematics
Osaka Kyoiku University
Kashiwara, Osaka 582-8582, Japan
e-mail

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