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

• Autorzy: Eiichi Nakai
• Języki publikacji: EN

Abstrakty

EN

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.

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 176
• Numer: 1
• Strony: 1-19

Daty

wydano

2006

Twórcy

autor

Eiichi Nakai

• Department of Mathematics, Osaka Kyoiku University, Kashiwara, Osaka 582-8582, Japan

Identyfikatory

DOI

10.4064/sm176-1-1