# Journal of theKorean Mathematical SocietyJKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

## Current Issue

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May, 2022 | Volume 59, No. 3
• ### 2022-05-01

#### The exceptional set of one prime square and five prime cubes

Yuhui Liu

Abstract : For a natural number $n$, let $R(n)$ denote the number of representations of $n$ as the sum of one square and five cubes of primes. In this paper, it is proved that the anticipated asymptotic formula for $R(n)$ fails for at most $O(N^{\frac{4}{9} + \varepsilon})$ positive integers not exceeding $N$.

• ### 2022-05-01

#### Zeros of new Bergman kernels

Noureddine Ghiloufi, Safa Snoun

Abstract : In this paper we determine explicitly the kernels $\mathbb K_{\alpha,\beta}$ associated with new Bergman spaces $\mathcal A_{\alpha,\beta}^2(\mathbb D)$ considered recently by the first author and M. Zaway. Then we study the distribution of the zeros of these kernels essentially when $\alpha\in\mathbb N$ where the zeros are given by the zeros of a real polynomial $Q_{\alpha,\beta}$. Some numerical results are given throughout the paper.

• ### 2022-05-01

#### Boundedness of Calder\'{o}n-Zygmund operators on inhomogeneous product Lipschitz spaces

Shaoyong He, Taotao Zheng

Abstract : In this paper, we study the boundedness of a class of inhomogeneous Journ\'{e}'s product singular integral operators on the inhomogeneous product Lipschitz spaces. The consideration of such inhomogeneous Journ\'{e}'s product singular integral operators is motivated by the study of the multi-parameter pseudo-differential operators. The key idea used here is to develop the Littlewood-Paley theory for the inhomogeneous product spaces which includes the characterization of a special inhomogeneous product Besov space and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.

• ### 2022-05-01

#### On weighted compactness of commutators of bilinear fractional maximal operator

Qianjun He, Juan Zhang

• ### 2022-05-01

#### A Neumann type problem on an unbounded domain in the Heisenberg group

Shivani Dubey, Mukund Madhav Mishra, Ashutosh Pandey

Abstract : We discuss the wellposedness of the Neumann problem on a half-space for the Kohn-Laplacian in the Heisenberg group. We then construct the Neumann function and explicitly represent the solution of the associated inhomogeneous problem.

• ### 2022-05-01

#### Erratum to Static and related critical spaces with harmonic curvature and three Ricci eigenvalues'' [J. Korean Math. Soc. 57 (2020), No. 6, pp. 1435--1449]

Jongsu Kim

Abstract : In this erratum, we offer a correction to [J. Korean Math. Soc. 57 (2020), No. 6, pp. 1435--1449]. Theorem 1 in the original paper has three assertions (i)-(iii), but we add (iv) after having clarified the argument.

## Current Issue

• ### Synchronized components of a subshift

Manouchehr Shahamat

J. Korean Math. Soc. 2022; 59(1): 1-12
https://doi.org/10.4134/JKMS.j200112

• ### Regularity of the generalized Poisson operator

Pengtao Li, Zhiyong Wang, Kai Zhao

J. Korean Math. Soc. 2022; 59(1): 129-150
https://doi.org/10.4134/JKMS.j210224

• ### Construction for self-orthogonal codes over a certain non-chain Frobenius ring

Boran Kim

J. Korean Math. Soc. 2022; 59(1): 193-204
https://doi.org/10.4134/JKMS.j210357

• ### Parabolic quaternionic Monge-Amp\{e}re equation on compact manifolds with a flat hyperK\"ahler metric

Jiaogen Zhang

J. Korean Math. Soc. 2022; 59(1): 13-33
https://doi.org/10.4134/JKMS.j200626

• ### Synchronized components of a subshift

Manouchehr Shahamat

J. Korean Math. Soc. 2022; 59(1): 1-12
https://doi.org/10.4134/JKMS.j200112

• ### Parabolic quaternionic Monge-Amp\{e}re equation on compact manifolds with a flat hyperK\"ahler metric

Jiaogen Zhang

J. Korean Math. Soc. 2022; 59(1): 13-33
https://doi.org/10.4134/JKMS.j200626

• ### Margin-based generalization for classifications with input noise

Hi Jun Choe, Hayeong Koh, Jimin Lee

J. Korean Math. Soc. 2022; 59(2): 217-233
https://doi.org/10.4134/JKMS.j200406

• ### Hardy type estimates for Riesz transforms associated with Schr\"{o}dinger operators on the Heisenberg group

Chunfang Gao

J. Korean Math. Soc. 2022; 59(2): 235-254
https://doi.org/10.4134/JKMS.j200484