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

作者：Mizuta Yoshihiro^*; Ohno Takao; Shimomura Tetsu

来源：Annales Academiae Scientiarum Fennicae-Mathematica, 2018, 43(1): 21-46.

DOI：10.5186/aasfm.2018.4302

• Spherical limits
• central Morrey Orlicz spaces
• Riesz potentials
• Green potentials

We introduce central Morrey-Orlicz spaces M-Phi,M-omega (B) on the unit ball and study the existence of weighted spherical limits:
lim inf(r -> 1-) (1 - r)(d1)omega(1 - r)(d2) (integral(S(0,r)) Phi((1 - r)(d3) vertical bar I(alpha)f(x)vertical bar)(q) dS(x))(1/q)
for some d(1), d(2), d(3) is an element of R, 1 <= q <= infinity, and all Riesz potentials I-alpha integral with integral is an element of M-Phi,M-omega(B). We also deal with the existence of weighted spherical limits for Green potentials and monotone Sobolev functions.

• 出版日期2018