Kehe Zhu
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Research Interests
Kehe Zhu has a total of 58 co-authors. Here are the top co-authors by number of shared publications:
- Hasi Wulan
Shantou University
7 shared publications - Guangfu Cao
School of Mathematics and Information Science, Guangzhou University, Guangzhou, China
6 shared publications - Guanlong Bao
Shantou University
6 shared publications - Chunjie Wang
Department of Mathematics, Hebei University of Technology, Tianjin, China
4 shared publications - Hong Rae Cho
Department of Mathematics, Pusan National University, Busan, Korea
3 shared publications - Jie Xiao
Department of Mathematics and Statistics, Memorial University, St. John’s, Canada
3 shared publications
Latest Publications
- 22 May 2026
- Published by Springer Nature in The Journal of Geometric Analysis
- Vol. 36 (7) , 233
Embedding and Compact Embedding Between Bergman and Hardy Spaces
- 22 May 2026
- Published by Springer Nature in The Journal of Geometric Analysis
- Vol. 36 (7) , 233
Embedding and Compact Embedding Between Bergman and Hardy Spaces
- 7 March 2026
- Published by Springer Nature in Potential Analysis
- Vol. 64 (3) , 51
Balayage for Weighted Bergman Spaces
- 7 March 2026
- Published by Springer Nature in Potential Analysis
- Vol. 64 (3) , 51
Balayage for Weighted Bergman Spaces
- 6 March 2026
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society
- Vol. 121 (1) , 28-52
WEIGHTED α -COMPOSITION AND RELATED FUNCTION SPACES
The notion of weighted $\alpha $ alpha -composition was introduced by Ruhan Zhao in the 1990s. In this paper, we study several analytic function spaces that are closely related to weighted $\alpha $ alpha -composition. These include $\alpha $ alpha -Bloch spaces, $F(p,q,s)$ upper F left parenthesis p comma q comma s right parenthesis spaces, and Campanato spaces. We obtain derivative-free characterizations for $\alpha $ alpha -Bloch spaces and $F(p,q,s)$ upper F left parenthesis p comma q comma s right parenthesis spaces, which improve some previous results in the literature. We also obtain a certain version of Carleson measures for Campanato spaces and $F(p,q,s)$ upper F left parenthesis p comma q comma s right parenthesis spaces.- 6 March 2026
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society
- Vol. 121 (1) , 28-52
WEIGHTED α -COMPOSITION AND RELATED FUNCTION SPACES
The notion of weighted $\alpha $ alpha -composition was introduced by Ruhan Zhao in the 1990s. In this paper, we study several analytic function spaces that are closely related to weighted $\alpha $ alpha -composition. These include $\alpha $ alpha -Bloch spaces, $F(p,q,s)$ upper F left parenthesis p comma q comma s right parenthesis spaces, and Campanato spaces. We obtain derivative-free characterizations for $\alpha $ alpha -Bloch spaces and $F(p,q,s)$ upper F left parenthesis p comma q comma s right parenthesis spaces, which improve some previous results in the literature. We also obtain a certain version of Carleson measures for Campanato spaces and $F(p,q,s)$ upper F left parenthesis p comma q comma s right parenthesis spaces.- Open Access
Deep zero problems and the HRT conjecture
We investigate a "deep zero problem" proposed by Hedenmalm. We show that there is a natural connection between Hedenmalm's problem and the classical HRT conjecture in time-frequency analysis. This connection allows us to show that Hedenmalm's problem 5.2 in [5] as well as some of its natural analogs have affirmative answers.
Open AccessDeep zero problems and the HRT conjecture
We investigate a "deep zero problem" proposed by Hedenmalm. We show that there is a natural connection between Hedenmalm's problem and the classical HRT conjecture in time-frequency analysis. This connection allows us to show that Hedenmalm's problem 5.2 in [5] as well as some of its natural analogs have affirmative answers.
- Open Access
Canonical integral operators on the Fock space II
In \cite{DZ3} we introduced and studied a two-parameter family of integral operators $T^{(s,t)}$ on the Fock space $F^2$ of the complex plane. Under the inverse Bargmann transform, these operators include the classical {\it linear canonical transforms} in mathematical physics as special cases, so we called $T^{(s,t)}$ {\it canonical linear operators} on the Fock space. In this paper we continue the study of these operators. We show that when a canonical linear operator $T^{(s,t)}$ is compact, it actually belongs to the Schatten class $S_p$ for all $p>0$. In this case, we find all singular values, determine the $S_p$ norm, and obtain a trace formula for $T^{(s,t)}$. We also show that the boundedness (and a natural version of compactness) of $T^{(s,t)}$ on $F^p$ for any given $p\in(0,\infty]$ is equivalent to the boundedness (and compactness) of $T^{(s,t)}$ on $F^2$. Our analysis is based on estimates and computations with the integral kernel of $T^{(s,t)}$, which also yield some interesting results about the Berezin transform and the bivariate Berezin transform of $T^{(s,t)}$.Open AccessCanonical integral operators on the Fock space II
In \cite{DZ3} we introduced and studied a two-parameter family of integral operators $T^{(s,t)}$ on the Fock space $F^2$ of the complex plane. Under the inverse Bargmann transform, these operators include the classical {\it linear canonical transforms} in mathematical physics as special cases, so we called $T^{(s,t)}$ {\it canonical linear operators} on the Fock space. In this paper we continue the study of these operators. We show that when a canonical linear operator $T^{(s,t)}$ is compact, it actually belongs to the Schatten class $S_p$ for all $p>0$. In this case, we find all singular values, determine the $S_p$ norm, and obtain a trace formula for $T^{(s,t)}$. We also show that the boundedness (and a natural version of compactness) of $T^{(s,t)}$ on $F^p$ for any given $p\in(0,\infty]$ is equivalent to the boundedness (and compactness) of $T^{(s,t)}$ on $F^2$. Our analysis is based on estimates and computations with the integral kernel of $T^{(s,t)}$, which also yield some interesting results about the Berezin transform and the bivariate Berezin transform of $T^{(s,t)}$. - 26 March 2025
- Published by Springer Nature
- p. 193-204
Best Kernel Approximation in Reproducing Kernel Hilbert Spaces
- 26 March 2025
- Published by Springer Nature
- p. 193-204
Best Kernel Approximation in Reproducing Kernel Hilbert Spaces
- Open Access
Embedding and compact embedding between Bergman and Hardy spaces
For Hardy spaces and weighted Bergman spaces on the open unit ball in ${\mathbb C}^n$, we determine exactly when $A^p_α\subset H^q$ or $H^p\subset A^q_α$, where $0<q<\infty$, $0<p<\infty$, and $-\infty<α<\infty$. For each such inclusion we also determine exactly when it is a compact embedding. Although some special cases were known before, we are able to completely cover all possible cases here. We also introduce a new notion called {\it tight fitting} and formulate a conjecture in terms of it, which places several prominent known results about contractive embeddings in the same framework.Open AccessEmbedding and compact embedding between Bergman and Hardy spaces
For Hardy spaces and weighted Bergman spaces on the open unit ball in ${\mathbb C}^n$, we determine exactly when $A^p_α\subset H^q$ or $H^p\subset A^q_α$, where $0<q<\infty$, $0<p<\infty$, and $-\infty<α<\infty$. For each such inclusion we also determine exactly when it is a compact embedding. Although some special cases were known before, we are able to completely cover all possible cases here. We also introduce a new notion called {\it tight fitting} and formulate a conjecture in terms of it, which places several prominent known results about contractive embeddings in the same framework. - 14 March 2024
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 152 (05) , 2131-2144
A 𝐶*-algebra of entire functions
We study the maximal abelian von Neumann algebra corresponding to L ∞ ( R ) L^\infty (\mathbb {R}) via the Bargmann transform. It is naturally an algebra of operators on the Fock space F 2 F^2 , but it can also be realized as a function algebra contained in F 2 F^2 . This provides an interesting example of a C ∗ C^* algebra whose elements are analytic functions.
- 14 March 2024
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 152 (05) , 2131-2144
A 𝐶*-algebra of entire functions
We study the maximal abelian von Neumann algebra corresponding to L ∞ ( R ) L^\infty (\mathbb {R}) via the Bargmann transform. It is naturally an algebra of operators on the Fock space F 2 F^2 , but it can also be realized as a function algebra contained in F 2 F^2 . This provides an interesting example of a C ∗ C^* algebra whose elements are analytic functions.
- 12 March 2024
- Published by Springer Nature in Mathematische Zeitschrift
- Vol. 306 (4) , 1-30
Canonical integral operators on the Fock space
- 12 March 2024
- Published by Springer Nature in Mathematische Zeitschrift
- Vol. 306 (4) , 1-30
Canonical integral operators on the Fock space
- 1 January 2024
- Published by Institute of Mathematics, Polish Academy of Sciences in Studia Mathematica
- Vol. 277 (2) , 99-122
Carleson measures for the Bloch space
We study the open problem of characterizing Carleson measures for the Bloch space. Several characterizations of these measures are obtained and several examples are constructed. Our approach is based on the theory of weighted Bergman spaces induced by cer
- 1 January 2024
- Published by Institute of Mathematics, Polish Academy of Sciences in Studia Mathematica
- Vol. 277 (2) , 99-122
Carleson measures for the Bloch space
We study the open problem of characterizing Carleson measures for the Bloch space. Several characterizations of these measures are obtained and several examples are constructed. Our approach is based on the theory of weighted Bergman spaces induced by cer