Bulletin of the
Korean Mathematical Society
BKMS
ISSN(Print) 1015-8634
ISSN(Online) 2234-3016
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2022-11-30
Estimate for bilinear Calder\'{o}n-Zygmund operator and its commutator on product of variable exponent spaces
Guanghui Lu, Shuangping TaoAbstract : The goal of this paper is to establish the boundedness of bilinear Calder\'{o}n-Zygmund operator $BT$ and its commutator $[b_{1},b_{2},BT]$ which is generated by $b_{1}, b_{2}\in\mathrm{BMO}(\mathbb{R}^{n})$ (or $\dot{\Lambda}_{\alpha}(\mathbb{R}^{n})$) and the $BT$ on generalized variable exponent Morrey spaces $\mathcal{L}^{p(\cdot),\varphi}(\mathbb{R}^{n})$. Under assumption that the functions $\varphi_{1}$ and $\varphi_{2}$ satisfy certain conditions, the authors proved that the $BT$ is bounded from product of spaces $\mathcal{L}^{p_{1}(\cdot),\varphi_{1}}(\mathbb{R}^{n}) \times\mathcal{L}^{p_{2}(\cdot),\varphi_{2}}(\mathbb{R}^{n})$ into space $\mathcal{L}^{p(\cdot),\varphi}(\mathbb{R}^{n})$. Furthermore, the boundedness of commutator $[b_{1},b_{2},BT]$ on spaces $L^{p(\cdot)}(\mathbb{R}^{n})$ and on spaces $\mathcal{L}^{p(\cdot),\varphi}(\mathbb{R}^{n})$ is also established.
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2023-01-31
S-curvature and geodesic orbit property of invariant $(\alpha_{1},\alpha_{2})$-metrics on spheres
Huihui An, Zaili Yan, Shaoxiang ZhangAbstract : Geodesic orbit spaces are homogeneous Finsler spaces whose geodesics are all orbits of one-parameter subgroups of isometries. Such Finsler spaces have vanishing S-curvature and hold the Bishop-Gromov volume comparison theorem. In this paper, we obtain a complete description of invariant $(\alpha_{1},\alpha_{2})$-metrics on spheres with vanishing S-curvature. Also, we give a description of invariant geodesic orbit $(\alpha_{1},\alpha_{2})$-metrics on spheres. We mainly show that a ${\mathrm S}{\mathrm p}(n+1)$-invariant $(\alpha_{1},\alpha_{2})$-metric on $\mathrm{S}^{4n+3}={\mathrm S}{\mathrm p}(n+1)/{\mathrm S}{\mathrm p}(n)$ is geodesic orbit with respect to ${\mathrm S}{\mathrm p}(n+1)$ if and only if it is ${\mathrm S}{\mathrm p}(n+1){\mathrm S}{\mathrm p}(1)$-invariant. As an interesting consequence, we find infinitely many Finsler spheres with vanishing S-curvature which are not geodesic orbit spaces.
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2022-09-30
Szeg\"{o} projections for Hardy spaces in quaternionic Clifford analysis
Fuli He
, Song Huang, Min KuAbstract : In this paper we study Szeg\"{o} kernel projections for Hardy spaces in quaternionic Clifford analysis. At first we introduce the matrix Szeg\"{o} projection operator for the Hardy space of quaternionic Hermitean monogenic functions by the characterization of the matrix Hilbert transform in the quaternionic Clifford analysis. Then we establish the Kerzman-Stein formula which closely connects the matrix Szeg\"{o} projection operator with the Hardy projection operator onto the Hardy space, and we get the matrix Szeg\"{o} projection operator in terms of the Hardy projection operator and its adjoint. At last, we construct the explicit matrix Szeg\"o kernel function for the Hardy space on the sphere as an example, and get the solution to a Diriclet boundary value problem for matrix functions.
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2022-07-31
The K\"{a}hler Different of a Set of Points in~$\mathbb{P}^{m}\!\times\mathbb{P}^{n}$
Nguyen T. Hoa, Tran N. K. Linh, Le N. Long, Phan T. T. Nhan, Nguyen T. P. NhiAbstract : Given an ACM set $\mathbb{X}$ of points in a multiprojective space $\mathbb{P}^{m}\!\times\mathbb{P}^{n}$ over a field of characteristic zero, we are interested in studying the K\"ahler different and the Cayley-Bacharach property for $\mathbb{X}$. In $\mathbb{P}^1\times \mathbb{P}^1$, the Cayley-Bacharach property agrees with the complete intersection property and it is characterized by using the K\"ahler different. However, this result fails to hold in $\mathbb{P}^{m}\!\times\mathbb{P}^{n}$ for $n>1$ or $m>1$. In this paper we start an investigation of the K\"ahler different and its Hilbert function and then prove that $\mathbb{X}$ is a complete intersection of type $(d_1,\ldots,d_m,d'_1,\ldots,d'_n)$ if and only if it has the Cayley-Bacharach property and the K\"ahler different is non-zero at a certain degree. We characterize the Cayley-Bacharach property of $\mathbb{X}$ under certain assumptions.
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2022-07-31
Starlike functions associated with a petal shaped domain
Kush Arora, S. Sivaprasad KumarAbstract : In this paper, we establish some radius results and inclusion relations for starlike functions associated with a petal-shaped domain.
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2023-01-31
Zero sums of dual Toeplitz products on the orthogonal complement of the Dirichlet space
Young Joo LeeAbstract : We consider dual Toeplitz operators acting on the orthogonal complement of the Dirichlet space on the unit disk. We give a characterization of when a finite sum of products of two dual Toeplitz operators is equal to $0$. Our result extends several known results by using a unified way.
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2022-11-30
Modified cyclotomic polynomials
Ae-Kyoung Cha, Miyeon Kwon, Ki-Suk Lee, Seong-Mo YangAbstract : Let $H$ be a subgroup of $\mathbb{Z}_n^\ast$ (the multiplicative group of integers modulo $n$) and $h_1,h_2,\ldots,h_l$ distinct representatives of the cosets of $H$ in $\mathbb{Z}_n^\ast$. We now define a polynomial $J_{n,H}(x)$ to be \begin{align*} \begin{split} J_{n,H}(x)=\prod\limits_{j=1}^{l} \bigg( x-\sum\limits_{h \in H}\zeta_n^{h_jh} \bigg), \end{split} \end{align*} where $\zeta_n=e^{\frac{2\pi i}{n}}$ is the $n$th primitive root of unity. Polynomials of such form generalize the $n$th cyclotomic polynomial $\Phi_n(x)=\prod_{k \in \mathbb{Z}_n^\ast}(x-\zeta_n^k)$ as $J_{n,\{1\}}(x)=\Phi_n(x)$. While the $n$th cyclotomic polynomial $\Phi_n(x)$ is irreducible over $\mathbb{Q}$, $J_{n,H}(x)$ is not necessarily irreducible. In this paper, we determine the subgroups $H$ for which $J_{n,H}(x)$ is irreducible over $\mathbb{Q}$.
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2022-07-31
Approximate projection algorithms for solving equilibrium and multivalued variational inequality problems in Hilbert space
Nguyen Minh Khoa, Tran Van ThangAbstract : In this paper, we propose new algorithms for solving equilibrium and multivalued variational inequality problems in a real Hilbert space. The first algorithm for equilibrium problems uses only one approximate projection at each iteration to generate an iteration sequence converging strongly to a solution of the problem underlining the bifunction is pseudomonotone. On the basis of the proposed algorithm for the equilibrium problems, we introduce a new algorithm for solving multivalued variational inequality problems. Some fundamental experiments are given to illustrate our algorithms as well as to compare them with other algorithms.
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2022-11-30
Tamed exhaustion functions and Schwarz type lemmas for almost Hermitian manifolds
Weike YuAbstract : In this paper, we study a special exhaustion function on almost Hermitian manifolds and establish the existence result by using the Hessian comparison theorem. From the viewpoint of the exhaustion function, we establish a related Schwarz type lemma for almost holomorphic maps between two almost Hermitian manifolds. As corollaries, we deduce several versions of Schwarz and Liouville type theorems for almost holomorphic maps.
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2022-09-30
N-pure ideals and mid rings
Mohsen AghajaniAbstract : In this paper, we introduce the concept of N-pure ideal as a generalization of pure ideal. Using this concept, a new and interesting type of rings is presented, we call it a mid ring. Also, we provide new characterizations for von Neumann regular and zero-dimensional rings. Moreover, some results about mp-ring are given. Finally, a characterization for mid rings is provided. Then it is shown that the class of mid rings is strictly between the class of reduced mp-rings (p.f.~rings) and the class of mp-rings.
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On the top local cohomology and formal local cohomology modules
Shahram Rezaei, Behrouz Sadeghi
Bull. Korean Math. Soc. 2023; 60(1): 149-160
https://doi.org/10.4134/BKMS.b220003 -
On the geometry of complex metallic Norden manifolds
Adara Monica Blaga, Rakesh Kumar, Rachna Rani
Bull. Korean Math. Soc. 2022; 59(5): 1069-1091
https://doi.org/10.4134/BKMS.b210190 -
Lipschitz type characterization of Fock type spaces
Hong Rae Cho, Jeong Min Ha
Bull. Korean Math. Soc. 2022; 59(6): 1371-1385
https://doi.org/10.4134/BKMS.b210783 -
Colocalization of generalized local homology modules
Marziyeh Hatamkhani
Bull. Korean Math. Soc. 2022; 59(4): 917-928
https://doi.org/10.4134/BKMS.b210534
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Existence of the continued fractions of $\sqrt{d}$ and its applications
Jun Ho Lee
Bull. Korean Math. Soc. 2022; 59(3): 697-707
https://doi.org/10.4134/BKMS.b210422 -
A new characterization of type $(A)$ and ruled real hypersurfaces in nonflat complex space forms
Yaning Wang
Bull. Korean Math. Soc. 2022; 59(4): 897-904
https://doi.org/10.4134/BKMS.b210514 -
On a generalization of unit regular rings
Tahire Ozen
Bull. Korean Math. Soc. 2023; 60(6): 1463-1475
https://doi.org/10.4134/BKMS.b220573 -
Fixed-width partitions according to the parity of the even parts
John Maxwell Campbell
Bull. Korean Math. Soc. 2023; 60(4): 1017-1024
https://doi.org/10.4134/BKMS.b220457
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