Abstract : Let $A$ be a general expansive matrix on $\mathbb{R}^n$ and $H_{A,w}^p(\mathbb R^n)$ the weighed anisotropic Hardy space associated to $A$, where $p\in(0,1]$ and $w$ is an anisotropic Muckenhoupt weight. In this article, the authors first introduce the weighted anisotropic Carleson measure space ${\mathrm{CMO}}_{A,w}^{p}(\mathbb{R}^n)$ in terms of wavelets. Then, using the known wavelet characterization of $H_{A,w}^p(\mathbb R^n)$ and establishing a duality relation between two sequence spaces, the authors prove that the space ${\mathrm{CMO}}_{A,w}^{p}(\mathbb{R}^n)$ is the dual space of $H_{A,w}^p(\mathbb R^n)$. As an application, the authors give a wavelet characterization of weighed anisotropic Campanato spaces. All these results are new even for the parabolic Hardy space or the anisotropic Hardy space $H_A^p(\mathbb R^n)$.
Abstract : This paper aims to study the harmonicity concerning the Berger-type Cheeger-Gromoll metric on the tangent bundle over an anti-paraK\"{a}hler manifold. Firstly, the harmonicity of a vector field is studied for this metric, and some examples of harmonic vector fields are. Secondly, the harmonicity of a vector field along a mapping between Riemannian manifolds has been discussed. The last section of this paper examines the harmonicity of the composition of the projection map of the tangent bundle of a Riemannina manifold with a map from this manifold into another Riemannian manifold.
Abstract : In this paper, we establish the half-plane analogue of P. Ahern and \v{Z}. \v{C}u\v{c}kovi\'{c} (1996) characterization of almost subharmonicity of functions satisfying the inequality $\mathcal{B}f\geq f$, where $\mathcal{B}$ denotes the Berezin transform. As a byproduct, we investigate hyponormality of a class of Toeplitz operators with bounded harmonic symbols acting on the Bergman space of the complex upper half-plane.
Hyungbin Park, Junsu Park
J. Korean Math. Soc. 2024; 61(5): 875-898
https://doi.org/10.4134/JKMS.j230053
Cédric Bonnafé, Alessandra Sarti
J. Korean Math. Soc. 2023; 60(4): 695-743
https://doi.org/10.4134/JKMS.j220014
Jangwon Ju
J. Korean Math. Soc. 2023; 60(5): 931-957
https://doi.org/10.4134/JKMS.j220231
Jaewook Ahn, Myeonghyeon Kim
J. Korean Math. Soc. 2023; 60(3): 619-634
https://doi.org/10.4134/JKMS.j220424
Jangwon Ju
J. Korean Math. Soc. 2023; 60(5): 931-957
https://doi.org/10.4134/JKMS.j220231
Cédric Bonnafé, Alessandra Sarti
J. Korean Math. Soc. 2023; 60(4): 695-743
https://doi.org/10.4134/JKMS.j220014
Hyungbin Park, Junsu Park
J. Korean Math. Soc. 2024; 61(5): 875-898
https://doi.org/10.4134/JKMS.j230053
Xing Yu Song, Ling Wu
J. Korean Math. Soc. 2023; 60(5): 1023-1041
https://doi.org/10.4134/JKMS.j220589
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