• 대한수학회보
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• 제45권2호
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• pp.321-338
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• 2008

Let $\bar{M}$ be a smoothly bounded pseudoconvex complex manifold with a family of almost complex structures $\{L^{\tau}\}_{{\tau}{\in}I}$, $0{\in}I$, which extend smoothly up to bM, the boundary of M, and assume that there is ${\lambda}{\in}C^{\infty}$(bM) which is strictly subharmonic with respect to the structure $L^0|_{bM}$ in any direction where the Levi-form vanishes on bM. We obtain explicit estimates for the $\bar{\partial}$-Neumann problem in Sobolev spaces both in space and parameter variables. Also we get a similar result when $\bar{M}$ is strongly pseudoconvex.

• Journal of applied mathematics & informatics
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• 제40권1_2호
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• pp.173-184
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• 2022

We investigated the invariant subspaces of the fractional integral operator in the Sobolev space W^k_p[0, 1] and prove unicellularity of the operator J^α by using the Duhamel product.

• East Asian mathematical journal
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• 제25권2호
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• pp.221-227
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• 2009

In this paper, we introduce the generalized H$\ddot{o}$lder space with a majorant function and prove the H$\ddot{o}$lder regularity for solutions of the Cauchy-Riemann equation in the generalized Holder spaces on a bounded convex domain in $\mathbb{C}^2$.

• 충청수학회지
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• 제1권1호
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• pp.27-32
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• 1988

In this paper, we study the multipliers of $A^p_q$ into $L^{p^{\prime}}$ when 0 < p' < p. For this purpose, we study the condition on the measure ${\mu}$ satisfying $A^p_q{\subset}A^{p^{\prime}}(d{\mu})$. It turns out that the quotient $k_q={\mu}/v_q$ over hyperbolic ball of radius less than 1 belongs to $L^s_q$, where $\frac{1}{s}+\frac{p^{\prime}}{p}=1$. For the proof, we replace the norm of $k_q$ by the Riemann sum, and then use a result of interpolation theory.