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Papers by Kamthorn Chailuek

Prince of Songkla Unversity. Faculty of Science

We consider the weighted Bergman spaces HL 2 (B d , µ λ), where we set dµ λ (z) = c λ (1−|z| 2) λ... more We consider the weighted Bergman spaces HL 2 (B d , µ λ), where we set dµ λ (z) = c λ (1−|z| 2) λ dτ (z), with τ being the hyperbolic volume measure. These spaces are nonzero if and only if λ > d. For 0 < λ ≤ d, spaces with the same formula for the reproducing kernel can be defined using a Sobolev-type norm. We define Toeplitz operators on these generalized Bergman spaces and investigate their properties. Specifically, we describe classes of symbols for which the corresponding Toeplitz operators can be defined as bounded operators or as a Hilbert-Schmidt operators on the generalized Bergman spaces.

Abstract. We consider the weighted Bergman spaces HL2(Bd, µλ), where we set dµλ(z) = cλ(1−|z|2)λ ... more Abstract. We consider the weighted Bergman spaces HL2(Bd, µλ), where we set dµλ(z) = cλ(1−|z|2)λ dτ(z), with τ being the hyperbolic volume measure. These spaces are nonzero if and only if λ> d. For 0 < λ ≤ d, spaces with the same formula for the reproducing kernel can be defined using a Sobolev-type norm. We define Toeplitz operators on these generalized Bergman spaces and investigate their properties. Specifically, we describe classes of symbols for which the corresponding Toeplitz operators can be defined as bounded oper-ators or as a Hilbert–Schmidt operators on the generalized Bergman spaces.

Sains Malaysiana, 2017

We obtain a generalization of Hardy's inequality for functions in the Hardy space H 1 (B d), wher... more We obtain a generalization of Hardy's inequality for functions in the Hardy space H 1 (B d), where B d is the unit ball {z = (z 1 , …, z d) ∈ In particular, we construct a function φ on the set of d-dimensional multi-indices {n = (n 1 , …, n d) | n i ∈   {0}} and prove that if f(z) = Σ a n z n is a function in H 1 (B d), then ≤ Moreover, our proof shows that this inequality is also valid for functions in Hardy space on the polydisk H 1 (B d).

Advances in Operator Theory, 2020

The generalized weighted Bergman space HðB d ; kÞ is defined as a reproducing kernel Hilbert spac... more The generalized weighted Bergman space HðB d ; kÞ is defined as a reproducing kernel Hilbert space of holomorphic functions on the open unit ball B d C d for all k [ 0. When k [ d, it is identical to the weighted Bergman space HL 2 ðB d ; l k Þ. We prove that the dual space HðB d ; aÞ Ã can be identified with another generalized weighted Bergman space HðB d ; bÞ under the pairing hf ; gi c ¼ R B d A k f ðzÞB k gðzÞ dl cþ2n ðzÞ; for f 2 HðB d ; aÞ; g 2 HðB d ; bÞ; where n ¼ d 2 AE Ç ; c ¼ aþb 2 and A k ; B k are operators related to the number operator N ¼ P d i¼1 z i o oz i :

Integral Equations and Operator Theory, 2010

We consider the weighted Bergman spaces HL 2 (B d , µ λ), where dµ λ (z) = c λ (1 − |z| 2) λ dτ (... more We consider the weighted Bergman spaces HL 2 (B d , µ λ), where dµ λ (z) = c λ (1 − |z| 2) λ dτ (z), τ being the hyperbolic volume measure. These spaces are nonzero if and only if λ > d. For 0 < λ ≤ d, spaces with the same formula for the reproducing kernel can be defined using a Sobolev-type norm. We define Toeplitz operators on these generalized Bergman spaces and investigate their properties. Specifically, we describe classes of symbols for which the corresponding Toeplitz operators can be defined as bounded operators or as a Hilbert-Schmidt operators on the generalized Bergman spaces.

Arxiv preprint math/0312341, 2003

Let U be a non-empty open subset of C. Denote by HL2(U, α) the space of all holomorphic functions... more Let U be a non-empty open subset of C. Denote by HL2(U, α) the space of all holomorphic functions on U which are square-integrable with respect to the measure α(ω)dω. For any t > 0, consider the Gaussian measure ... Then the space HL2(C,µt) is called the Segal-Bargmann space. ...

For a given positive in teger n, we can count the number of incongruent triangles with integer si... more For a given positive in teger n, we can count the number of incongruent triangles with integer sides and perimeter n. In this article, we classify this number into the number of equilateral, isosceles and scalene triangles which have integer sides and perimeter n.

Prince of Songkla Unversity. Faculty of Science

We consider the weighted Bergman spaces HL 2 (B d , µ λ), where we set dµ λ (z) = c λ (1−|z| 2) λ... more We consider the weighted Bergman spaces HL 2 (B d , µ λ), where we set dµ λ (z) = c λ (1−|z| 2) λ dτ (z), with τ being the hyperbolic volume measure. These spaces are nonzero if and only if λ > d. For 0 < λ ≤ d, spaces with the same formula for the reproducing kernel can be defined using a Sobolev-type norm. We define Toeplitz operators on these generalized Bergman spaces and investigate their properties. Specifically, we describe classes of symbols for which the corresponding Toeplitz operators can be defined as bounded operators or as a Hilbert-Schmidt operators on the generalized Bergman spaces.

Abstract. We consider the weighted Bergman spaces HL2(Bd, µλ), where we set dµλ(z) = cλ(1−|z|2)λ ... more Abstract. We consider the weighted Bergman spaces HL2(Bd, µλ), where we set dµλ(z) = cλ(1−|z|2)λ dτ(z), with τ being the hyperbolic volume measure. These spaces are nonzero if and only if λ> d. For 0 < λ ≤ d, spaces with the same formula for the reproducing kernel can be defined using a Sobolev-type norm. We define Toeplitz operators on these generalized Bergman spaces and investigate their properties. Specifically, we describe classes of symbols for which the corresponding Toeplitz operators can be defined as bounded oper-ators or as a Hilbert–Schmidt operators on the generalized Bergman spaces.

Sains Malaysiana, 2017

We obtain a generalization of Hardy's inequality for functions in the Hardy space H 1 (B d), wher... more We obtain a generalization of Hardy's inequality for functions in the Hardy space H 1 (B d), where B d is the unit ball {z = (z 1 , …, z d) ∈ In particular, we construct a function φ on the set of d-dimensional multi-indices {n = (n 1 , …, n d) | n i ∈   {0}} and prove that if f(z) = Σ a n z n is a function in H 1 (B d), then ≤ Moreover, our proof shows that this inequality is also valid for functions in Hardy space on the polydisk H 1 (B d).

Advances in Operator Theory, 2020

The generalized weighted Bergman space HðB d ; kÞ is defined as a reproducing kernel Hilbert spac... more The generalized weighted Bergman space HðB d ; kÞ is defined as a reproducing kernel Hilbert space of holomorphic functions on the open unit ball B d C d for all k [ 0. When k [ d, it is identical to the weighted Bergman space HL 2 ðB d ; l k Þ. We prove that the dual space HðB d ; aÞ Ã can be identified with another generalized weighted Bergman space HðB d ; bÞ under the pairing hf ; gi c ¼ R B d A k f ðzÞB k gðzÞ dl cþ2n ðzÞ; for f 2 HðB d ; aÞ; g 2 HðB d ; bÞ; where n ¼ d 2 AE Ç ; c ¼ aþb 2 and A k ; B k are operators related to the number operator N ¼ P d i¼1 z i o oz i :

Integral Equations and Operator Theory, 2010

We consider the weighted Bergman spaces HL 2 (B d , µ λ), where dµ λ (z) = c λ (1 − |z| 2) λ dτ (... more We consider the weighted Bergman spaces HL 2 (B d , µ λ), where dµ λ (z) = c λ (1 − |z| 2) λ dτ (z), τ being the hyperbolic volume measure. These spaces are nonzero if and only if λ > d. For 0 < λ ≤ d, spaces with the same formula for the reproducing kernel can be defined using a Sobolev-type norm. We define Toeplitz operators on these generalized Bergman spaces and investigate their properties. Specifically, we describe classes of symbols for which the corresponding Toeplitz operators can be defined as bounded operators or as a Hilbert-Schmidt operators on the generalized Bergman spaces.

Arxiv preprint math/0312341, 2003

Let U be a non-empty open subset of C. Denote by HL2(U, α) the space of all holomorphic functions... more Let U be a non-empty open subset of C. Denote by HL2(U, α) the space of all holomorphic functions on U which are square-integrable with respect to the measure α(ω)dω. For any t > 0, consider the Gaussian measure ... Then the space HL2(C,µt) is called the Segal-Bargmann space. ...

For a given positive in teger n, we can count the number of incongruent triangles with integer si... more For a given positive in teger n, we can count the number of incongruent triangles with integer sides and perimeter n. In this article, we classify this number into the number of equilateral, isosceles and scalene triangles which have integer sides and perimeter n.