In [2], P. Oswald discussed the approximation behaviours of the Bochner-Riesz means above critical index of the Fourier integrals of the functions in H^p(R) (0<p≤1) and obtained a Jacson-type inequality. The inequ...In [2], P. Oswald discussed the approximation behaviours of the Bochner-Riesz means above critical index of the Fourier integrals of the functions in H^p(R) (0<p≤1) and obtained a Jacson-type inequality. The inequality was based on equivalence of the H^p(R)-modulus of continuity and the corresponding K-functional.展开更多
The author establishes operator-valued Fourier multiplier theorems on multi-dimensional Hardy spaces Hp(Td;X),where 1 ≤ p < ∞,d ∈ N,and X is an AUMD Banach space having the property (α).The suffcient condition ...The author establishes operator-valued Fourier multiplier theorems on multi-dimensional Hardy spaces Hp(Td;X),where 1 ≤ p < ∞,d ∈ N,and X is an AUMD Banach space having the property (α).The suffcient condition on the multiplier is a Marcinkiewicz type condition of order 2 using Rademacher boundedness of sets of bounded linear operators.It is also shown that the assumption that X has the property (α) is necessary when d ≥ 2 even for scalar-valued multipliers.When the underlying Banach space does not have the property (α),a suffcient condition on the multiplier of Marcinkiewicz type of order 2 using a notion of d-Rademacher boundedness is also given.展开更多
In the paper,we study derivative estimates of the iterated spherical averages(At)^(N)(f).We obtain the optimal range of exponents(α,N,p)to ensure the L^(p)boundedness of P(■/■x)(A1)^(N)(f)for 1≤p≤∞,where P is a ...In the paper,we study derivative estimates of the iterated spherical averages(At)^(N)(f).We obtain the optimal range of exponents(α,N,p)to ensure the L^(p)boundedness of P(■/■x)(A1)^(N)(f)for 1≤p≤∞,where P is a homogeneous polynomial of degree a.The main theorem extends some known results.As an application,we obtain the smallest N such that(A1)^(N):L^(p)(R^(n))→L_(α)^(p)(R^(n)).展开更多
We proved if k(z)∈ Hª(q≥ 1),g(z) is analytic on| ≠ = 1, g(e)+ k(e") q= min g(e")+ h(e)heHq, then k' (z)∈ H' , especially, if q1, then k(z) is an analytic function on the closed unit disk| ≠1.
文摘In [2], P. Oswald discussed the approximation behaviours of the Bochner-Riesz means above critical index of the Fourier integrals of the functions in H^p(R) (0<p≤1) and obtained a Jacson-type inequality. The inequality was based on equivalence of the H^p(R)-modulus of continuity and the corresponding K-functional.
基金Project supported by the National Natural Science Foundation of China (No. 10731020)the Specialized Research Fund for the Doctoral Program of Higher Education (No. 200800030059)
文摘The author establishes operator-valued Fourier multiplier theorems on multi-dimensional Hardy spaces Hp(Td;X),where 1 ≤ p < ∞,d ∈ N,and X is an AUMD Banach space having the property (α).The suffcient condition on the multiplier is a Marcinkiewicz type condition of order 2 using Rademacher boundedness of sets of bounded linear operators.It is also shown that the assumption that X has the property (α) is necessary when d ≥ 2 even for scalar-valued multipliers.When the underlying Banach space does not have the property (α),a suffcient condition on the multiplier of Marcinkiewicz type of order 2 using a notion of d-Rademacher boundedness is also given.
基金Supported by National Natural Science Foundation of China (Grant Nos. 11771388, 11371316)the Natural Science Foundation of Zhejiang (Grant No. LQ20A010003)
文摘In the paper,we study derivative estimates of the iterated spherical averages(At)^(N)(f).We obtain the optimal range of exponents(α,N,p)to ensure the L^(p)boundedness of P(■/■x)(A1)^(N)(f)for 1≤p≤∞,where P is a homogeneous polynomial of degree a.The main theorem extends some known results.As an application,we obtain the smallest N such that(A1)^(N):L^(p)(R^(n))→L_(α)^(p)(R^(n)).
文摘We proved if k(z)∈ Hª(q≥ 1),g(z) is analytic on| ≠ = 1, g(e)+ k(e") q= min g(e")+ h(e)heHq, then k' (z)∈ H' , especially, if q1, then k(z) is an analytic function on the closed unit disk| ≠1.
