Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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 ℝⁿ case. Let (X,d,μ) be a space of homogeneous type and (X,δ,μ) its normalized space in the sense of Macías and Segovia. We also study the relations of these function spaces for (X,d,μ) and for (X,δ,μ). 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.
Słowa kluczowe
Kategorie tematyczne
- 46E15: Banach spaces of continuous, differentiable or analytic functions
- 42B35: Function spaces arising in harmonic analysis
- 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
- 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
Czasopismo
Rocznik
Tom
Numer
Strony
1-19
Opis fizyczny
Daty
wydano
2006
Twórcy
autor
- Department of Mathematics, Osaka Kyoiku University, Kashiwara, Osaka 582-8582, Japan
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-sm176-1-1