Inclusion Relations for New Function Spaces on Riemann Surfaces
Canadian mathematical bulletin, Tome 56 (2013) no. 3, pp. 466-476

Voir la notice de l'article provenant de la source Cambridge University Press

We introduce and study some new function spaces on Riemann surfaces. For certain parameter values these spaces coincide with the classical Dirichlet space, $\text{BMOA}$ , or the recently defined ${{\text{Q}}_{p}}$ space. We establish inclusion relations that generalize earlier known inclusions between the above-mentioned spaces.
DOI : 10.4153/CMB-2012-005-6
Mots-clés : 0F35, 30H25, 30H30, Bloch space, BMOA, Qp, Green's function, hyperbolic Riemann surface
Aulaskari, Rauno; Rättyä, Jouni. Inclusion Relations for New Function Spaces on Riemann Surfaces. Canadian mathematical bulletin, Tome 56 (2013) no. 3, pp. 466-476. doi: 10.4153/CMB-2012-005-6
@article{10_4153_CMB_2012_005_6,
     author = {Aulaskari, Rauno and R\"atty\"a, Jouni},
     title = {Inclusion {Relations} for {New} {Function} {Spaces} on {Riemann} {Surfaces}},
     journal = {Canadian mathematical bulletin},
     pages = {466--476},
     year = {2013},
     volume = {56},
     number = {3},
     doi = {10.4153/CMB-2012-005-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-005-6/}
}
TY  - JOUR
AU  - Aulaskari, Rauno
AU  - Rättyä, Jouni
TI  - Inclusion Relations for New Function Spaces on Riemann Surfaces
JO  - Canadian mathematical bulletin
PY  - 2013
SP  - 466
EP  - 476
VL  - 56
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-005-6/
DO  - 10.4153/CMB-2012-005-6
ID  - 10_4153_CMB_2012_005_6
ER  - 
%0 Journal Article
%A Aulaskari, Rauno
%A Rättyä, Jouni
%T Inclusion Relations for New Function Spaces on Riemann Surfaces
%J Canadian mathematical bulletin
%D 2013
%P 466-476
%V 56
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-005-6/
%R 10.4153/CMB-2012-005-6
%F 10_4153_CMB_2012_005_6

[1] [1] Aulaskari, R. and Chen, H., Area inequality and Qp norm. J. Funct. Anal. 221 (2005), no. 1, 1–24. Google Scholar | DOI

[2] [2] Aulaskari, R., He, Y., Ristioja, J., and Zhao, R., Qp spaces on Riemann surfaces. Canad. J. Math. 50 (1998), no. 3, 449–464. Google Scholar | DOI

[3] [3] Aulaskari, R. and Lappan, P., A criterion for a rotation automorphic function to be normal. Bull. Inst. Math. Acad. Sinica 15 (1987), no. 1, 73–79. Google Scholar

[4] [4] Aulaskari, R., Lappan, P., Xiao, J., and Zhao, R., BMOA(R;m) and capacity density Bloch spaces on hyperbolic Riemann surfaces. Results Math. 29 (1996), no. 3–4, 203–226. Google Scholar

[5] [5] Kobayashi, S., Range sets and BMO norms of analytic functions. Canad. J. Math. 36 (1984), no. 4, 747–755. Google Scholar | DOI

[6] [6] Kobayashi, S. and Suita, N., Area integrals and Hp norms of analytic functions. Complex Variables Theory Appl. 5 (1986), no. 2–4, 181–188. Google Scholar | DOI

[7] [7] Metzger, T. A., On BMOA for Riemann surfaces. Canad. J. Math. 33 (1981), no. 5, 1255–1260. Google Scholar | DOI

[8] [8] Minda, D., Bloch and normal functions on general planar regions. In: Holomorphic functions and moduli, Vol. I (Berkeley, CA, 1986), Math. Sci. Res. Inst. Publ., 10, Springer, New York, 1988), pp. 101–110. Google Scholar

[9] [9] Rubel, L. and Timoney, R., An extremal property of the Bloch space. Proc. Amer. Math. Soc. 75 (1979), no. 1, 45–49. Google Scholar | DOI

[10] [10] Stoll, M., A characterization of Hardy-Orlicz spaces on planar domains. Proc. Amer. Math. Soc. 117 (1993), no. 4, 1031–1038. Google Scholar | DOI

[11] [11] Tsuji, M., Potential theory in modern function theory. Maruzen Co., Ltd., Tokyo, 1959). Google Scholar

[12] [12] Zhao, R., An exponential decay characterization of BMOA on Riemann surfaces. Arch. Math. (Basel) 79 (2002), no. 1, 61–66. Google Scholar | DOI

[13] [13] Zhao, R., The characteristics of BMOA on Riemann surfaces. Kodai Math. J. 15 (1992), no. 2, 221–229. Google Scholar | DOI

Cité par Sources :