Article
Keywords:
weighted spaces; harmonic functions; integral representation; isometry
Summary:
The paper establishes integral representation formulas in arbitrarily wide Banach spaces $b^p_\omega(\Bbb R^n)$ of functions harmonic in the whole $\Bbb R^n$.
References:
[1] Petrosyan A.I.:
On weighted classes of harmonic functions in the unit ball of $\bold R^n$. Complex Var. Theory Appl. 50 12 (2005), 953-966.
MR 2164690
[2] Petrosyan A.I.:
On $A^p_ømega$ spaces in the unit ball of $\Bbb C^n$. J. Anal. Appl. 3 1 47-53 (2005).
MR 2110499
[3] Djrbashian M.M.: On canonical representation of functions meromorphic in the unit disc (in Russian). Dokl. Akad. Nauk of Armenia (1945), 3 1 3-9.
[4] Djrbashian M.M.: On the representability problem of analytic functions (in Russian). Soobsch. Inst. Math. and Mech. AN Armenii 2 (1948), 3-40.
[5] Jerbashian A.M.:
On the theory of weighted classes of area integrable regular functions. Complex Var. Theory Appl. 50 3 155-183 (2005).
MR 2123953 |
Zbl 1081.46024
[7] Axler S., Bourdon P., Ramsey W.:
Harmonic Function Theory. Springer, New York, 2001.
MR 1805196