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Growth properties for generalized Riesz potentials of functions satisfying Orlicz conditions |
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| Authors: | Yoshihiro Mizuta Takao Ohno Tetsu Shimomura Yusuke Yamauchi |
| Affiliation: | 1. 4-13-11 Hachi-Hom-Matsu-Minami, Higashi-Hiroshima, 739-0144 Japan;2. Faculty of Education, Oita University, Dannoharu Oita-city, 870-1192 Japan;3. Department of Mathematics, Graduate School of Education, Hiroshima University, Higashi-Hiroshima, 739-8524 Japan;4. Department of Intelligent Mechanical Engineering, Hiroshima Institute of Technology, 2-1-1 Miyake Saeki-ku, Hiroshima, 731-5193 Japan |
| Abstract: | Riesz decomposition theorem says that superharmonic functions on the punctured unit ball are represented as the sum of generalized (Newtonian) potentials and harmonic functions. In this paper we study growth properties near the origin of spherical means for generalized Riesz potentials of functions satisfying Orlicz conditions in the punctured unit ball. |
| Keywords: | generalized Riesz potentials Orlicz conditions spherical limits |