In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order t...In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order to prove the main results,we first give some bidirectional estimates for several typical integrals.展开更多
Let Ω be a domain in C^(n) and let Y be a function space on Ω.If a∈Ω and g∈Y with g(a)=0,do there exist functions f_(1),f_(2),…,f_(n)∈Y such that g(z)=∑_(l=1)^(n)(z_(l)−a_(l))f_(l)(z)for all z=(z_(1),z_(2),…,...Let Ω be a domain in C^(n) and let Y be a function space on Ω.If a∈Ω and g∈Y with g(a)=0,do there exist functions f_(1),f_(2),…,f_(n)∈Y such that g(z)=∑_(l=1)^(n)(z_(l)−a_(l))f_(l)(z)for all z=(z_(1),z_(2),…,z_(n))∈Ω?This is Gleason’s problem.In this paper,we prove that Gleason’s problem is solvable on the boundary general function space F^(p,q,s)(B)in the unit ball B of C^(n).展开更多
基金supported by the Natural Science Foundation of Hunan Province of China(2022JJ30369)the Education Department Important Foundation of Hunan Province in China(23A0095)。
文摘In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order to prove the main results,we first give some bidirectional estimates for several typical integrals.
基金supported by the National Natural Science Foundation of China(11942109)the Natural Science Foundation of Hunan Province(2022JJ30369).
文摘Let Ω be a domain in C^(n) and let Y be a function space on Ω.If a∈Ω and g∈Y with g(a)=0,do there exist functions f_(1),f_(2),…,f_(n)∈Y such that g(z)=∑_(l=1)^(n)(z_(l)−a_(l))f_(l)(z)for all z=(z_(1),z_(2),…,z_(n))∈Ω?This is Gleason’s problem.In this paper,we prove that Gleason’s problem is solvable on the boundary general function space F^(p,q,s)(B)in the unit ball B of C^(n).
