Geodesic
Some characterizations of harmonic Bloch and Besov spaces
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 417-430 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The relationship between weighted Lipschitz functions and analytic Bloch spaces has attracted much attention. In this paper, we define harmonic $\omega $-$\alpha $-Bloch space and characterize it in terms of $$ \omega ((1-|x|^2)^\beta (1-|y|^2)^{\alpha - \beta }) \Big | \frac {f(x)-f(y)}{x-y}\Big | $$ and $$ \omega ((1-|x|^2)^\beta (1-|y|^2)^{\alpha - \beta }) \Big | \frac {f(x)-f(y)}{|x|y-x'}\Big | $$ where $\omega $ is a majorant. Similar results are extended to harmonic little $\omega $-$\alpha $-Bloch and Besov spaces. Our results are generalizations of the corresponding ones in G. Ren, U. Kähler (2005).
The relationship between weighted Lipschitz functions and analytic Bloch spaces has attracted much attention. In this paper, we define harmonic $\omega $-$\alpha $-Bloch space and characterize it in terms of $$ \omega ((1-|x|^2)^\beta (1-|y|^2)^{\alpha - \beta }) \Big | \frac {f(x)-f(y)}{x-y}\Big | $$ and $$ \omega ((1-|x|^2)^\beta (1-|y|^2)^{\alpha - \beta }) \Big | \frac {f(x)-f(y)}{|x|y-x'}\Big | $$ where $\omega $ is a majorant. Similar results are extended to harmonic little $\omega $-$\alpha $-Bloch and Besov spaces. Our results are generalizations of the corresponding ones in G. Ren, U. Kähler (2005).
DOI : 10.1007/s10587-016-0265-y
Classification : 30C20, 31B05, 32A18
Keywords: harmonic function; Bloch space; Besov space; majorant 
@article{10_1007_s10587_016_0265_y,
     author = {Fu, Xi and Lu, Bowen},
     title = {Some characterizations of harmonic {Bloch} and {Besov} spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {417--430},
     year = {2016},
     volume = {66},
     number = {2},
     doi = {10.1007/s10587-016-0265-y},
     mrnumber = {3519611},
     zbl = {06604476},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-016-0265-y/}
}
TY  - JOUR
AU  - Fu, Xi
AU  - Lu, Bowen
TI  - Some characterizations of harmonic Bloch and Besov spaces
JO  - Czechoslovak Mathematical Journal
PY  - 2016
SP  - 417
EP  - 430
VL  - 66
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-016-0265-y/
DO  - 10.1007/s10587-016-0265-y
LA  - en
ID  - 10_1007_s10587_016_0265_y
ER  - 
%0 Journal Article
%A Fu, Xi
%A Lu, Bowen
%T Some characterizations of harmonic Bloch and Besov spaces
%J Czechoslovak Mathematical Journal
%D 2016
%P 417-430
%V 66
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-016-0265-y/
%R 10.1007/s10587-016-0265-y
%G en
%F 10_1007_s10587_016_0265_y
Fu, Xi; Lu, Bowen. Some characterizations of harmonic Bloch and Besov spaces. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 417-430. doi: 10.1007/s10587-016-0265-y

Cité par Sources :