• 충청수학회지
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• 제22권2호
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• pp.287-291
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• 2009

A comparison of constants is given to show that a better constant for the Sobolev trace inequality can be obtained from the conjectured extremal function.

• 충청수학회지
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• 제21권4호
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• pp.493-499
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• 2008

We construct a minimizing sequence for the Sobolev trace inequality which satises compactness in the concentration compactness property.

• 대한수학회보
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• 제57권5호
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• pp.1143-1149
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• 2020

Sobolev trace inequalities on nonhomogeneous fractional Sobolev spaces are established.

• 대한수학회보
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• 제37권2호
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• pp.303-316
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• 2000

The Cauchy problem for degenerate parabolic equations with absorption is studied. We prove the existence of a fundamental solution. Also a Harnack type inequality is established and the existence and uniqueness of initial trace for nonnegative solutions is shown.

• Korean Journal of Mathematics
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• 제24권2호
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• pp.273-296
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• 2016

Some new trace inequalities for convex functions of self-adjoint operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated. Some trace inequalities for matrices are also derived. Examples for the operator power and logarithm are presented as well.

• 대한수학회지
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• 제46권3호
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• pp.523-550
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• 2009

In the paper two-weight inequalities of various type for strong fractional maximal functions and potentials with multiple kernels defined on $\mathbb{R}^2$ are established.

• 대한수학회보
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• 제53권3호
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• pp.875-884
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• 2016

Let x : $^{Mn-1}{\rightarrow}{\mathbb{R}}^n$ ($n{\geq}4$) be an umbilical free hyper-surface with non-zero principal curvatures. Then x is associated with a Laguerre metric g, a Laguerre tensor L, a Laguerre form C, and a Laguerre second fundamental form B, which are invariants of x under Laguerre transformation group. We denote the Laguerre scalar curvature by R and the trace-free Laguerre tensor by ${\tilde{L}}:=L-{\frac{1}{n-1}}tr(L)g$. In this paper, we prove a local classification result under the assumption of parallel Laguerre form and an inequality of the type $${\parallel}{\tilde{L}}{\parallel}{\leq}cR$$ where $c={\frac{1}{(n-3){\sqrt{(n-2)(n-1)}}}$ is appropriate real constant, depending on the dimension.

• Korean Journal of Mathematics
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• 제27권2호
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• pp.375-415
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• 2019

We study spaces of continuous-function-valued functions that have the property that composition with evaluation functionals induce $weak^*$ to norm continuous maps to ${\ell}^p$ space ($p{\in}(1,\;{\infty})$). Versions of $H{\ddot{o}}lder^{\prime}s$ inequality and Riesz representation theorem are proved to hold on these spaces. We prove a version of Dixmier's theorem for spaces of function-valued matrix operators on these spaces, and an analogue of the trace formula for operators on Hilbert spaces. When the function space is taken to be the complex field, the spaces are just the ${\ell}^p$ spaces and the well-known classical theorems follow from our results.