The Harmonic Bloch and Besov Spaces on the Real Unit Ball by an Oscillation
LetBbe the real unit ball inRnandf∈CN(B). Given a multi-indexm=(m1,…,mn)of nonnegative integers with|m|=N, we set the quantitysupx∈B,y∈E(x,r),x≠y(1-|x|2)α(1-|y|2)β|∂mf(x)-∂mf(y)|/|x-y|γ[x,y]1-γ, x≠y,where0≤γ≤1andα+β=N+1. In terms of it, we characterize harmonic Bloch and Besov spaces on the real unit ball. This generalizes the main results of Yoneda, 2002, into real harmonic setting.
2005 ◽
Vol 48
(3)
◽
pp. 743-755
◽
2014 ◽
Vol 34
(3)
◽
pp. 629-638
◽
2001 ◽
Vol 44
(1)
◽
pp. 1-12
◽
2010 ◽
Vol 216
(12)
◽
pp. 3541-3549
◽
2009 ◽
Vol 7
(3)
◽
pp. 209-223
◽
Keyword(s):
2009 ◽
Vol 7
(1)
◽
pp. 91-104
◽
Keyword(s):
1995 ◽
Vol 189
(2)
◽
pp. 533-551
◽
2001 ◽
Vol 31
(4)
◽
pp. 1305-1316
◽