Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 21-46

GROWTH PROPERTIES OF POTENTIALS IN CENTRAL MORREY–ORLICZ SPACES ON THE UNIT BALL

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. We introduce central Morrey–Orlicz spaces M^Φ,ω(B) on the unit ball and study the existence of weighted spherical limits:

liminf_r→1- (1 – r)^d1ω(1 – r)^d2(∫_S(0,r) Φ((1 – r)^d3|I_αf(x)|)^q dS(x))^1/q

for some d₁, d₂, d₃ ∈ R, 1 ≤ q < ∞, and all Riesz potentials I_αf with f ∈ M^Φ,ω(B). We also deal with the existence of weighted spherical limits for Green potentials and monotone Sobolev functions.

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

Key words: Spherical limits, central Morrey–Orlicz spaces, Riesz potentials, Green potentials.

Reference to this article: Y. Mizuta, T. Ohno and T. Shimomura: Growth properties of potentials in central Morrey–Orlicz spaces on the unit ball. Ann. Acad. Sci. Fenn. Math. 43 (2018), 21-46.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4302