• Bulletin of the Korean Mathematical Society
• /
• v.57 no.4
• /
• pp.851-864
• /
• 2020

This paper gives a sparse domination for the iterated commutators of multilinear pseudo-differential operators with the symbol σ belonging to the Hörmander class, and establishes the quantitative bounds of the Bloom type estimates for such commutators. Moreover, the C_p estimates for the corresponding multilinear pseudo-differential operators are also obtained.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.2
• /
• pp.679-686
• /
• 2017

The present paper is devoted to self-adjoint cyclically compact operators on Hilbert-Kaplansky module over a ring of bounded measurable functions. The spectral theorem for such a class of operators is given. We use more simple and constructive method, which allowed to apply this result to compact operators relative to von Neumann algebras. Namely, a general form of compact operators relative to a type I von Neumann algebra is given.

• Honam Mathematical Journal
• /
• v.40 no.1
• /
• pp.125-138
• /
• 2018

In this present paper, we deal with the generalized (k, s)-fractional integral and differential operators recently defined by Nisar et al. and obtain some generalized (k, s)-fractional integral and differential formulas involving the class of a function as its kernels. Also, we investigate a certain number of their consequences containing the said function in their kernels.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.4
• /
• pp.957-969
• /
• 2023

Let j be a nonnegative integer. We define the Toeplitz-type operators T^(j)_a with symbol a ∈ L^∞(C), which are variants of the traditional Toeplitz operators obtained for j = 0. In this paper, we study the boundedness of these operators and characterize their compactness in terms of its Berezin transform.

• Journal of the Korean Mathematical Society
• /
• v.48 no.6
• /
• pp.1203-1223
• /
• 2011

In this paper, the authors investigate the structure of operators similar to normaloid and transloid operators. In particular, we characterize the interior of the set of operators similar to normaloid (transloid, respectively) operators. This gives a concise spectral condition to determine when an operator is similar to a normaloid or transloid operator. Also it is proved that any Hilbert space operator has a compact perturbation with transloid property. This is used to give a negative answer to a problem posed by W. Y. Lee, concerning Weyl's theorem.

• Communications of the Korean Mathematical Society
• /
• v.27 no.3
• /
• pp.621-627
• /
• 2012

Star operations are defined by R. E. Hodel in 1994. In this paper some relations among star operators, sequential closure operators and closure operators are discussed. Moreover, we introduce an induced topology by a family of subsets of a space, and some interesting results about star operators are established by the induced topology.

• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.2
• /
• pp.269-286
• /
• 2015

In this paper, we extend the concept of the pseudo differential operators in the usual Schwartz's distribution spaces to the one of the generalized pseudo differential operators in the Beurling's generalized distribution spaces. And we shall investigate some properties of the generalized pseudo differential operators including the generalized pseudo local property. Finally, we will study the smoothness and properly supported property of these operators.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.3
• /
• pp.747-761
• /
• 2017

We study multiplication operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm. In addition, we determine the spectrum of the bounded multiplication operators and characterize the isometries. Finally, we study the multiplication operators between the weighted Banach spaces and the Lipschitz space by characterizing the bounded and the compact operators, determining estimates on the operator norm, and showing there are no isometries.

• Communications of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.1249-1269
• /
• 2018

This paper provides a method to study the nonnegativity of certain linear operators, from other operators with similar spectral properties. If these new operators are formally self-adjoint and nonnegative, we can study the complex powers using an appropriate locally convex space. In this case, the initial operator also will be nonnegative and we will be able to study its powers. In particular, we have applied this method to Bessel-type operators.

• Communications of the Korean Mathematical Society
• /
• v.37 no.1
• /
• pp.91-103
• /
• 2022

In this paper, we introduce Toeplitz operators and Hankel operators with complex Borel measures on the closed unit disk. When a positive measure 𝜇 on (-1, 1) is a Carleson measure, it is known that the corresponding Hankel matrix is bounded and vice versa. We show that for a positive measure 𝜇 on 𝔻, 𝜇 is a Carleson measure if and only if the Toeplitz operator with symbol 𝜇 is a densely defined bounded linear operator. We also study Hankel operators of Hilbert-Schmidt class.