Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 125-140

BOUNDARY GROWTH OF GENERALIZED RIESZ POTENTIALS ON THE UNIT BALL IN THE VARIABLE SETTINGS

Yoshihiro Mizuta, Takao Ohno and Tetsu Shimomura

4-13-11 Hachi-Hon-Matsu-Minami, Higashi-Hiroshima 739-0144, Japan; yomizuta 'at' hiroshima-u.ac.jp

Oita University, Faculty of Education
Dannoharu Oita-city 870-1192, Japan; t-ohno 'at' oita-u.ac.jp

Hiroshima University, Graduate School of Education, Department of Mathematics
Higashi-Hiroshima 739-8524, Japan; tshimo 'at' hiroshima-u.ac.jp

Abstract. Riesz decomposition theorem says that a superharmonic function is locally represented as the sum of a potential and a harmonic function. In this paper we introduce a generalized Riesz kernel and study the boundary growth for its potential as an extension of Gardiner [3] in the variable settings.

2010 Mathematics Subject Classification: Primary 31B15, 46E35.

Key words: Variable exponent, spherical means, superharmonic functions, generalized Riesz potentials.

Reference to this article: Y. Mizuta, T. Ohno and T. Shimomura: Boundary growth of generalized Riesz potentials on the unit ball in the variable settings. Ann. Acad. Sci. Fenn. Math. 44 (2019), 125-140.

Full document as PDF file

https://doi.org/10.5186/aasfm.2019.4403