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

Eiichi Nakai. "The Campanato, Morrey and Hölder spaces on spaces of homogeneous type." Studia Mathematica 176.1 (2006): 1-19. <http://eudml.org/doc/285029>.

@article{EiichiNakai2006,
abstract = {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.},
author = {Eiichi Nakai},
journal = {Studia Mathematica},
keywords = {Morrey space; Campanatto space; Hölder space; space of homogeneous type; bounded mean oscillation},
language = {eng},
number = {1},
pages = {1-19},
title = {The Campanato, Morrey and Hölder spaces on spaces of homogeneous type},
url = {http://eudml.org/doc/285029},
volume = {176},
year = {2006},
}

TY - JOUR
AU - Eiichi Nakai
TI - The Campanato, Morrey and Hölder spaces on spaces of homogeneous type
JO - Studia Mathematica
PY - 2006
VL - 176
IS - 1
SP - 1
EP - 19
AB - 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.
LA - eng
KW - Morrey space; Campanatto space; Hölder space; space of homogeneous type; bounded mean oscillation
UR - http://eudml.org/doc/285029
ER -