Some characterizations of harmonic Bloch and Besov spaces
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 417-430.

Voir la notice de l'article dans Czech Digital Mathematics Library

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
Mots-clés : 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},
     publisher = {mathdoc},
     volume = {66},
     number = {2},
     year = {2016},
     doi = {10.1007/s10587-016-0265-y},
     mrnumber = {3519611},
     zbl = {06604476},
     language = {en},
     url = {https://geodesic-test.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
PB  - mathdoc
UR  - https://geodesic-test.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
%I mathdoc
%U https://geodesic-test.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. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0265-y/

Cité par Sources :