Boundedness of Generalized Parametric Marcinkiewicz Integrals Associated to Surfaces
Keyword(s):
In this article, the boundedness of the generalized parametric Marcinkiewicz integral operators M Ω , ϕ , h , ρ ( r ) is considered. Under the condition that Ω is a function in L q ( S n - 1 ) with q ∈ ( 1 , 2 ] , appropriate estimates of the aforementioned operators from Triebel–Lizorkin spaces to L p spaces are obtained. By these estimates and an extrapolation argument, we establish the boundedness of such operators when the kernel function Ω belongs to the block space B q 0 , ν - 1 ( S n - 1 ) or in the space L ( l o g L ) ν ( S n - 1 ) . Our results represent improvements and extensions of some known results in generalized parametric Marcinkiewicz integrals.
2015 ◽
Vol 99
(3)
◽
pp. 380-398
◽
Keyword(s):
2004 ◽
Vol 2004
(72)
◽
pp. 4001-4011
Keyword(s):
2003 ◽
Vol 46
(3)
◽
pp. 669-677
◽
2002 ◽
Vol 72
(1)
◽
pp. 13-22
◽