In this paper, we obtain certain Lpw（Rn）-mapping properties for the maximal operator associated with the commutators of quasiradial Bochner-Riesz means with index δ under certain surface condition on Σed , provide...In this paper, we obtain certain Lpw（Rn）-mapping properties for the maximal operator associated with the commutators of quasiradial Bochner-Riesz means with index δ under certain surface condition on Σed , provided that δ （n-1）/2, b ∈ BMO（Rn）, 1 p ∞ and w ∈ A1 . Moreover, if δ （n-1）/2, then we prove that the above maximal operator admits weak type （H1w（Rn）, L1w（Rn））-mapping properties for b ∈ BMO（Rn） and w ∈ A1 under the surface condition on Σed .展开更多
Let M be a complete non-compact Riemannian manifold satisfying the volume doubling property and the Gaussian upper bounds. Denote by A the Laplace-Beltrami operator and by V the Riemannian gradient. In this paper, the...Let M be a complete non-compact Riemannian manifold satisfying the volume doubling property and the Gaussian upper bounds. Denote by A the Laplace-Beltrami operator and by V the Riemannian gradient. In this paper, the author proves the weighted reverse inequality ｜｜Δ^1/2f｜｜L^p（w）×C｜｜｜Δ↓｜｜｜L^p（w）, for some range ofp determined by M and w. Moreover, a weak type estimate is proved when p = 1. Some weighted vector-valued inequalities are also established.展开更多
We have pointed out in [1] that so far the L^2 norm inequalities with power weights for the Riesz means σ_R~δ(g)(x) of multiple Fourier integrals have been obtained only by Hirschman and J. L. Rubio de Francia respe...We have pointed out in [1] that so far the L^2 norm inequalities with power weights for the Riesz means σ_R~δ(g)(x) of multiple Fourier integrals have been obtained only by Hirschman and J. L. Rubio de Francia respectively:展开更多
基金Supported by School of Education, Korea University Grant in 2011
文摘In this paper, we obtain certain Lpw（Rn）-mapping properties for the maximal operator associated with the commutators of quasiradial Bochner-Riesz means with index δ under certain surface condition on Σed , provided that δ （n-1）/2, b ∈ BMO（Rn）, 1 p ∞ and w ∈ A1 . Moreover, if δ （n-1）/2, then we prove that the above maximal operator admits weak type （H1w（Rn）, L1w（Rn））-mapping properties for b ∈ BMO（Rn） and w ∈ A1 under the surface condition on Σed .
基金supported by the China Scholarship Council(No.201406100171)
文摘Let M be a complete non-compact Riemannian manifold satisfying the volume doubling property and the Gaussian upper bounds. Denote by A the Laplace-Beltrami operator and by V the Riemannian gradient. In this paper, the author proves the weighted reverse inequality ｜｜Δ^1/2f｜｜L^p（w）×C｜｜｜Δ↓｜｜｜L^p（w）, for some range ofp determined by M and w. Moreover, a weak type estimate is proved when p = 1. Some weighted vector-valued inequalities are also established.
文摘We have pointed out in [1] that so far the L^2 norm inequalities with power weights for the Riesz means σ_R~δ(g)(x) of multiple Fourier integrals have been obtained only by Hirschman and J. L. Rubio de Francia respectively:
