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1
Content available remote

Oscillatory kernels in certain Hardy-type spaces

100%
Chen L.-K., Fan D.
Studia Mathematica
|
1994
|
tom 111
|
nr 2
195-206
EN
We consider a convolution operator Tf = p.v. Ω ⁎ f with $Ω(x) = K(x)e^{ih(x)}$, where K(x) is an (n,β) kernel near the origin and an (α,β), α ≥ n, kernel away from the origin; h(x) is a real-valued $C^∞$ function on $ℝ^n ∖ {0}$. We give a criterion for such an operator to be bounded from the space $H^{p}_{0}(ℝ^n)$ into itself.
2
Content available remote

Multiplier transformations on $H^{p}$ spaces

100%
Chen D., Fan D.
Studia Mathematica
|
1998
|
tom 131
|
nr 2
189-204
EN
The authors obtain some multiplier theorems on $H^p$ spaces analogous to the classical $L^p$ multiplier theorems of de Leeuw. The main result is that a multiplier operator $(Tf)^(x) = λ(x)f̂(x)$ $(λ ∈ C(ℝ^n))$ is bounded on $H^p(ℝ^n)$ if and only if the restriction ${λ(εm)}_{m∈Λ}$ is an $H^p(T^n)$ bounded multiplier uniformly for ε>0, where Λ is the integer lattice in $ℝ^n$.
3
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Boundedness of certain oscillatory singular integrals

100%
Fan D., Pan Y.
Studia Mathematica
|
1995
|
tom 114
|
nr 2
105-116
EN
We prove the $L^p$ and $H^1$ boundedness of oscillatory singular integral operators defined by Tf = p.v.Ω∗f, where $Ω(x) = e^{iΦ(x)}K(x)$, K(x) is a Calderón-Zygmund kernel, and Φ satisfies certain growth conditions.
4
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Weighted weak type (1,1) estimates for singular integrals and Littlewood-Paley functions

100%
Fan D., Sato S.
Studia Mathematica
|
2004
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tom 163
|
nr 2
119-136
EN
We prove some weighted weak type (1,1) inequalities for certain singular integrals and Littlewood-Paley functions.
5
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The method of rotation and Marcinkiewicz integrals on product domains

81%
Chen J., Fan D., Ying Y.
Studia Mathematica
|
2002
|
tom 153
|
nr 1
41-58
EN
We give some rather weak sufficient condition for $L^{p}$ boundedness of the Marcinkiewicz integral operator $μ_{Ω}$ on the product spaces $ℝⁿ × ℝ^{m}$ (1 < p < ∞), which improves and extends some known results.
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