In this paper,the authors obtain the Dunkl analogy of classical L^(p)Hardy inequality for p>N+2γwith sharp constant((p-N-2γ)/p)^(p),where 2γis the degree of weight function associated with Dunkl operators,and L ...In this paper,the authors obtain the Dunkl analogy of classical L^(p)Hardy inequality for p>N+2γwith sharp constant((p-N-2γ)/p)^(p),where 2γis the degree of weight function associated with Dunkl operators,and L pHardy inequalities with distant function in some G-invariant domains.Moreover they prove two Hardy-Rellich type inequalities for Dunkl operators.展开更多
We consider the local boundary values of generalized harmonic functions associated with the rank-one Dunkl operator D in the upper half-plane R2+=R×(0,∞),where(Df)(x)=f′0(x)+(λ/x)[f(x)-f(-x)]for givenλ≥0.A C...We consider the local boundary values of generalized harmonic functions associated with the rank-one Dunkl operator D in the upper half-plane R2+=R×(0,∞),where(Df)(x)=f′0(x)+(λ/x)[f(x)-f(-x)]for givenλ≥0.A C2 function u in R2+is said to beλ-harmonic if(D2x+■2y)u=0.For aλ-harmonic function u in R2+and for a subset E of■R2+=R symmetric about y-axis,we prove that the following three assertions are equivalent:(i)u has a finite non-tangential limit at(x,0)for a.e.x∈E;(ii)u is non-tangentially bounded for a.e.x∈E;(iii)(Su)(x)<∞for a.e.x∈E,where S is a Lusin-type area integral associated with the Dunkl operator D.展开更多
Abstract The aim of this paper is to prove duality and reflexivity of generalized Lipschitz spaces ∧κα,p,q（R）, α ∈R and 1≤〈 p, q ≤∞, in the context of Dunkl harmonic analysis.
In this paper, we consider the generalized translations associated with the Dunkl and the Jacobi-Dunkl differential-difference operators on the real line which provide the structure of signed hrpergroups on R. Especia...In this paper, we consider the generalized translations associated with the Dunkl and the Jacobi-Dunkl differential-difference operators on the real line which provide the structure of signed hrpergroups on R. Especially, we study the representation of the gener- alized translations of the product of two functions for these signed hypergroups.展开更多
In the framework of superspace in Clifford analysis for the Dunkl version,the Fischer decomposition is established for solutions of the Dunkl super Dirac operators.The result is general without restrictions on multipl...In the framework of superspace in Clifford analysis for the Dunkl version,the Fischer decomposition is established for solutions of the Dunkl super Dirac operators.The result is general without restrictions on multiplicity functions or on super dimensions.The Fischer decomposition provides a module for the Howe dual pair G×osp(1|2)on the space of spinor valued polynomials with G the Coxeter group,while the generators of the Lie superspace reveal the naturality of the Fischer decomposition.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11771395,12071431)
文摘In this paper,the authors obtain the Dunkl analogy of classical L^(p)Hardy inequality for p>N+2γwith sharp constant((p-N-2γ)/p)^(p),where 2γis the degree of weight function associated with Dunkl operators,and L pHardy inequalities with distant function in some G-invariant domains.Moreover they prove two Hardy-Rellich type inequalities for Dunkl operators.
基金the National Natural Science Foundation of China(No.11371258).
文摘We consider the local boundary values of generalized harmonic functions associated with the rank-one Dunkl operator D in the upper half-plane R2+=R×(0,∞),where(Df)(x)=f′0(x)+(λ/x)[f(x)-f(-x)]for givenλ≥0.A C2 function u in R2+is said to beλ-harmonic if(D2x+■2y)u=0.For aλ-harmonic function u in R2+and for a subset E of■R2+=R symmetric about y-axis,we prove that the following three assertions are equivalent:(i)u has a finite non-tangential limit at(x,0)for a.e.x∈E;(ii)u is non-tangentially bounded for a.e.x∈E;(iii)(Su)(x)<∞for a.e.x∈E,where S is a Lusin-type area integral associated with the Dunkl operator D.
文摘Abstract The aim of this paper is to prove duality and reflexivity of generalized Lipschitz spaces ∧κα,p,q（R）, α ∈R and 1≤〈 p, q ≤∞, in the context of Dunkl harmonic analysis.
文摘In this paper, we consider the generalized translations associated with the Dunkl and the Jacobi-Dunkl differential-difference operators on the real line which provide the structure of signed hrpergroups on R. Especially, we study the representation of the gener- alized translations of the product of two functions for these signed hypergroups.
基金supported by the Unidade de Investigao"Matemtica e Aplicaoes"of University of AveiroNational Natural Science Foundation of China(Grant No.10771201)support by Ghent University and expresses his sincere gratitude to Prof.F.Brackx,H.De Schepper,and F.Sommen for the kind hospitality during the visit
文摘In the framework of superspace in Clifford analysis for the Dunkl version,the Fischer decomposition is established for solutions of the Dunkl super Dirac operators.The result is general without restrictions on multiplicity functions or on super dimensions.The Fischer decomposition provides a module for the Howe dual pair G×osp(1|2)on the space of spinor valued polynomials with G the Coxeter group,while the generators of the Lie superspace reveal the naturality of the Fischer decomposition.
