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"Kim, Joonil"
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Multiple Hilbert transforms associated with polynomials
Contents:Introduction Definitions of polyhedra, their faces and cones Main theorem and background Combinatorial lemmas Descending faces vs. ascending cones Preliminary results of analysis Proof of sufficiency Necessity theorem Preliminary lemmas for necessity proof Proof of necessity Proofs of Corollary 3.1 and main Theorem 3.1 Appendix Bibliography
eBook
Sublevel-Set Estimates Over Global Domains
Since Varchenko’s seminal paper, the asymptotics of oscillatory integrals and related problems have been elucidated through the Newton polyhedra associated with the phase
P
. The supports of those integrals are concentrated on sufficiently small neighborhoods. The aim of this paper is to investigate the estimates of sublevel sets and oscillatory integrals whose supports are global domains
D
. A basic model of
D
is
R
d
. For this purpose, we define the Newton polyhedra associated with (
P
,
D
) and establish analogues of Varchenko’s theorem in global domains
D
, under nondegeneracy conditions of
P
.
Journal Article
Maximal functions associated to a family of flat curves in lacunary directions
Consider the maximal operator defined by
M
γ
a
f
(
x
1
,
x
2
)
=
sup
k
∈
Z
sup
r
>
0
1
2
r
∫
-
r
r
|
f
(
x
1
-
t
,
x
2
-
a
k
γ
(
t
)
)
|
d
t
,
where
{
(
t
,
γ
(
t
)
)
}
is a convex curve and
a
=
(
a
k
)
is a lacunary sequence. We observe that
γ
′
doubling assumption does not imply to the
L
p
boundedness of
M
γ
a
. However, under the infinitesimally doubling condition on
γ
′
, we obtain the
L
p
boundedness of
M
γ
a
for all
1
<
p
<
∞
.
Journal Article
Maximal operators along flat curves with one variable vector field
We study a maximal average along a family of curves $\\{(t,m(x_1)\\gamma(t)):t\\in [-r,r]\\}$, where $\\gamma|_{[0,\\infty)}$ is a convex function and m is a measurable function. Under the assumption of the doubling property of $\\gamma'$ and $1\\leqslant m(x_1)\\leqslant 2$, we prove the $L^p(\\mathbb{R}^2)$ boundedness of the maximal average. As a corollary, we obtain the pointwise convergence of the average in r > 0 without any size assumption for a measurable m.
Journal Article
Dividend Policy and Corporate Social Responsibility: A Comparative Analysis of Multinational Enterprise Subsidiaries and Domestic Firms in Korea
In this study, we compare and contrast the dividend policies of multinational enterprise (MNE) subsidiaries with local firms in Korea and extract implications for corporate social responsibility (CSR). We find empirical evidence that dividend policies of MNE subsidiaries in Korea are in general determined to meet remittance requirements imposed by their parent company and have weak correlation with local CSR and investment requirements for wealth creation by local stakeholders.
Journal Article
Circular maximal functions on the Heisenberg group
We prove the \\(L^p\\) boundedness of the circular maximal function on the Heisenberg group \\(\\mathbb{H}^1\\) for \\(2
Paper
Sublevel Set Estimates over Global Domains
Since Varchenko's seminal paper, the asymptotics of oscillatory integrals and related problems have been elucidated through the Newton polyhedra associated with the phase \\(P\\). The supports of those integrals are concentrated on sufficiently small neighborhoods. The aim of this paper is to investigate the estimates of sub-level-sets and oscillatory integrals whose supports are global domains \\(D\\). A basic model of \\(D\\) is \\( \\mathbb{R}^d\\). For this purpose, we define the Newton polyhedra associated with \\((P,D)\\) and establish analogues of Varchenko's theorem in global domains \\(D\\), under non-degeneracy conditions of \\(P\\).
Paper
Discrete Double Hilbert Transforms Along Polynomial Surfaces
We obtain a necessary and sufficient condition on a polynomial \\(P(t_1,t_2)\\) for the \\(\\ell^{p}\\) boundedness of the discrete double Hilbert transforms associated with \\(P(t)\\) for \\(1 < p < \\infty\\). The proof is based on the multi-parameter circle method treating the cases of \\(|t_1|\\not\\approx |t_2|\\) arising from \\(1/t_1\\) and \\(1/t_2\\).
Paper
Restricted weak type endpoint estimate for the spherical maximal operators on the Heisenberg group
Let \\(\\mathbb{H}^n\\) denote the Heisenberg group, identified with \\(\\mathbb{R}^d \\times \\mathbb{R}\\), where \\(d = 2n\\) and \\(n \\in \\mathbb{N}\\). We consider the spherical maximal operator \\(\\mathcal{M}\\) associated with the sphere \\(S^{d-1}\\) embedded in the horizontal subspace \\(\\mathbb{R}^d \\times \\{0\\}\\) of \\(\\mathbb{H}^n\\). It is known that \\(\\mathcal{M}\\) is bounded on \\(L^p(\\mathbb{H}^n)\\) if and only if \\(p \\in (\\tfrac{d}{d-1}, \\infty]\\). In this paper, we establish a restricted weak type \\((p,p)\\) estimate at the endpoint \\(p = \\tfrac{d}{d-1}\\) for \\(\\mathcal{M}\\), provided \\(d \\ge 3\\).
Paper