Fan Dashan, Lu Shanzhen, Pan Yibiao
Suppose that {α
k}
k∞=-∞ is a Lacunary sequance of positive numbers satisfying inf
and that Ω(
y') is a function in the Besov space
B10,1 (
Sn-1) where
Sn-1 is the unit sphere on R
n(n≥2). We prove that if ∫S
n-1Ω(y')dσ(y') then the discrete singular integral operator
and the associated maximal operator
are both bounded in the space
L2(R
n)
The theorems in this paper improve a result by Duoandikoetxea and Rubio de Francia[1] in the L2 case.