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SOME CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH TWISTED CONVOLUTION
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 79 / Issue 3 / June 2009
- Published online by Cambridge University Press:
- 17 April 2009, pp. 405-417
- Print publication:
- June 2009
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A problem on rough parametric Marcinkiewicz functions
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 72 / Issue 1 / February 2002
- Published online by Cambridge University Press:
- 09 April 2009, pp. 13-22
- Print publication:
- February 2002
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In this note the authors give the L2(
n) boundedness of a class of parametric Marcinkiewicz integral 
with kernel function Ω in L log+L(Sn−1) and radial function h(|x|) ∈ l ∞ l(Lq)(
+) for 1 < q ≦.As its corollary, the Lp (
n)(2 < p < ∞) boundedness of and 
and 
with Ω in L log+L (Sn-1) and h(|x|) ∈ l∞ (Lq)(
+) are also obtained. Here 
and 
are parametric Marcinkiewicz functions corresponding to the Littlewood-Paley g*λ-function and the Lusin area function S, respectively.
with kernel function Ω in 
+) for 1 < q ≦.
and 
with Ω in 
and 
are parametric Marcinkiewicz functions corresponding to the Littlewood-Paley 