In this article, we study LP-boundedness properties of the oscillation and vari- ation operators for the heat and Poissson semigroup and Riesz transforms in the Laguerre settings. Also, we characterize Hardy spaces as...In this article, we study LP-boundedness properties of the oscillation and vari- ation operators for the heat and Poissson semigroup and Riesz transforms in the Laguerre settings. Also, we characterize Hardy spaces associated to Laguerre operators by using the variation operator of the heat semigroup.展开更多
For n E N, let On be the semigroup of all singular order-preserving mappings on [n] = （1, 2,..., n}. For each nonempty subset A of [n], let On （A） = （a ∈ On： （A k ∈ A） ka ≤ k} be the semigroup of all order-p...For n E N, let On be the semigroup of all singular order-preserving mappings on [n] = （1, 2,..., n}. For each nonempty subset A of [n], let On （A） = （a ∈ On： （A k ∈ A） ka ≤ k} be the semigroup of all order-preserving and A-decreasing mappings on [n]. In this paper it is shown that On（A）is an abundant semigroup with n - 1 ＊-classes. Moreover, On（A） is idempotent-generated and its idempotent rank is 2n - 2 - IA／（n}l. Further, it is shown that the rank of On（A） is equal to n - 1 if 1 ∈ A, and it is equal to n otherwise.展开更多
The α-times integrated C semigroups, α > 0, are introduced and analyzed. The Laplace inverse transformation for α-times integrated C semigroups is obtained, some known results are generalized.
Let Tx be the full transformation semigroup on a set X. For a non-trivial equivalence F on X, letTF（X） = {f ∈ Tx ： arbieary （x, y） ∈ F, （f（x）,f（y）） ∈ F}.Then TF（X） is a subsemigroup of Tx. Let E be ano...Let Tx be the full transformation semigroup on a set X. For a non-trivial equivalence F on X, letTF（X） = {f ∈ Tx ： arbieary （x, y） ∈ F, （f（x）,f（y）） ∈ F}.Then TF（X） is a subsemigroup of Tx. Let E be another equivalence on X and TFE（X） = TF（X） ∩ TE（X）. In this paper, under the assumption that the two equivalences F and E are comparable and E lohtain in F, we describe the regular elements and characterize Green＇s relations for the semigroup TFE（X）.展开更多
For an infinite set X, denote by Ω(X) the semigroup of all surjective mappings from X to X. We determine Green's relations in Ω(X), show that the kernel (unique minimum ideal) of Ω(X) exists and det ermine its ...For an infinite set X, denote by Ω(X) the semigroup of all surjective mappings from X to X. We determine Green's relations in Ω(X), show that the kernel (unique minimum ideal) of Ω(X) exists and det ermine its elemen ts and cardinali ty. For a cou ntably infinite set X, we describe the elements of Ω(X) for which the D-class and J-class coincide. We compare the results for Ω(X) with the corresponding results for other transformation semigroups on X.展开更多
Let V be a linear space over a field F with finite dimension,L(V) the semigroup,under composition,of all linear transformations from V into itself.Suppose that V = V1⊕V2⊕···⊕Vm is a direct sum decomp...Let V be a linear space over a field F with finite dimension,L(V) the semigroup,under composition,of all linear transformations from V into itself.Suppose that V = V1⊕V2⊕···⊕Vm is a direct sum decomposition of V,where V1,V2,...,Vm are subspaces of V with the same dimension.A linear transformation f ∈ L(V) is said to be sum-preserving,if for each i(1 ≤ i ≤ m),there exists some j(1 ≤ j ≤ m) such that f(Vi) ■Vj.It is easy to verify that all sum-preserving linear transformations form a subsemigroup of L(V) which is denoted by L⊕(V).In this paper,we first describe Green's relations on the semigroup L⊕(V).Then we consider the regularity of elements and give a condition for an element in L⊕(V) to be regular.Finally,Green's equivalences for regular elements are also characterized.展开更多
基金supported by Ministerio de Educación y Ciencia (Spain),grant MTM 2007-65609supported by Ministerio de Educacióon y Ciencia (Spain),grant MTM 2008-06621-C02supported by Universidad Nacional del Comahue (Argentina) and Ministerio de Educación y Ciencia (Spain) grant PCI 2006-A7-0670
文摘In this article, we study LP-boundedness properties of the oscillation and vari- ation operators for the heat and Poissson semigroup and Riesz transforms in the Laguerre settings. Also, we characterize Hardy spaces associated to Laguerre operators by using the variation operator of the heat semigroup.
文摘For n E N, let On be the semigroup of all singular order-preserving mappings on [n] = （1, 2,..., n}. For each nonempty subset A of [n], let On （A） = （a ∈ On： （A k ∈ A） ka ≤ k} be the semigroup of all order-preserving and A-decreasing mappings on [n]. In this paper it is shown that On（A）is an abundant semigroup with n - 1 ＊-classes. Moreover, On（A） is idempotent-generated and its idempotent rank is 2n - 2 - IA／（n}l. Further, it is shown that the rank of On（A） is equal to n - 1 if 1 ∈ A, and it is equal to n otherwise.
文摘The α-times integrated C semigroups, α > 0, are introduced and analyzed. The Laplace inverse transformation for α-times integrated C semigroups is obtained, some known results are generalized.
基金the Natural Science Found of Henan Province (No.0511010200)the Doctoral Fund of Henan Polytechnic University (No.2009A110007)the Natural Science Research Project for Education Department of Henan Province (No.2009A110007)
文摘Let Tx be the full transformation semigroup on a set X. For a non-trivial equivalence F on X, letTF（X） = {f ∈ Tx ： arbieary （x, y） ∈ F, （f（x）,f（y）） ∈ F}.Then TF（X） is a subsemigroup of Tx. Let E be another equivalence on X and TFE（X） = TF（X） ∩ TE（X）. In this paper, under the assumption that the two equivalences F and E are comparable and E lohtain in F, we describe the regular elements and characterize Green＇s relations for the semigroup TFE（X）.
文摘For an infinite set X, denote by Ω(X) the semigroup of all surjective mappings from X to X. We determine Green's relations in Ω(X), show that the kernel (unique minimum ideal) of Ω(X) exists and det ermine its elemen ts and cardinali ty. For a cou ntably infinite set X, we describe the elements of Ω(X) for which the D-class and J-class coincide. We compare the results for Ω(X) with the corresponding results for other transformation semigroups on X.
文摘Let V be a linear space over a field F with finite dimension,L(V) the semigroup,under composition,of all linear transformations from V into itself.Suppose that V = V1⊕V2⊕···⊕Vm is a direct sum decomposition of V,where V1,V2,...,Vm are subspaces of V with the same dimension.A linear transformation f ∈ L(V) is said to be sum-preserving,if for each i(1 ≤ i ≤ m),there exists some j(1 ≤ j ≤ m) such that f(Vi) ■Vj.It is easy to verify that all sum-preserving linear transformations form a subsemigroup of L(V) which is denoted by L⊕(V).In this paper,we first describe Green's relations on the semigroup L⊕(V).Then we consider the regularity of elements and give a condition for an element in L⊕(V) to be regular.Finally,Green's equivalences for regular elements are also characterized.
