Let G be a locally compact Abelian group with Haar measure μ. In the present paper, first the authors discussed some properties of weighted Lorentz space. Then they defined the relative completion A of a subspace A o...Let G be a locally compact Abelian group with Haar measure μ. In the present paper, first the authors discussed some properties of weighted Lorentz space. Then they defined the relative completion A of a subspace A of the weighted Lorentz space, and showed that the space of the multipliers from L_w~1,(G) to A is algebrically isomorphic and homeomorphic to A.展开更多
In this paper, we investigate the space of <em>L<sup>p</sup> p</em>-harmonic 1-forms on a complete noncompact orientable <em>δ</em>-stable hypersurface <em>M<sup>m</...In this paper, we investigate the space of <em>L<sup>p</sup> p</em>-harmonic 1-forms on a complete noncompact orientable <em>δ</em>-stable hypersurface <em>M<sup>m</sup></em> that is immersed in space form <img src="Edit_6fbc11b9-ac23-40e2-b045-0fb25419337d.png" width="35" height="23" alt="" /> with nonnegative BiRic curvature. We prove the nonexistence of <em>L<sup>p</sup> p</em>-harmonic 1-forms on <em>M<sup>m</sup></em>. Moreover, we obtain some vanishing properties for this class of harmonic 1-forms.展开更多
In this paper, the complete moment convergence for L~p-mixingales are studied.Sufficient conditions are given for the complete moment convergence for the maximal partial sums of B-valued L~p-mixingales by utilizing th...In this paper, the complete moment convergence for L~p-mixingales are studied.Sufficient conditions are given for the complete moment convergence for the maximal partial sums of B-valued L~p-mixingales by utilizing the Rosenthal maximal type inequality for B-valued martingale difference sequence, which extend and improve the related known works in the literature.展开更多
文摘Let G be a locally compact Abelian group with Haar measure μ. In the present paper, first the authors discussed some properties of weighted Lorentz space. Then they defined the relative completion A of a subspace A of the weighted Lorentz space, and showed that the space of the multipliers from L_w~1,(G) to A is algebrically isomorphic and homeomorphic to A.
文摘In this paper, we investigate the space of <em>L<sup>p</sup> p</em>-harmonic 1-forms on a complete noncompact orientable <em>δ</em>-stable hypersurface <em>M<sup>m</sup></em> that is immersed in space form <img src="Edit_6fbc11b9-ac23-40e2-b045-0fb25419337d.png" width="35" height="23" alt="" /> with nonnegative BiRic curvature. We prove the nonexistence of <em>L<sup>p</sup> p</em>-harmonic 1-forms on <em>M<sup>m</sup></em>. Moreover, we obtain some vanishing properties for this class of harmonic 1-forms.
基金supported by the National Science Foundation of China(11271161)
文摘In this paper, the complete moment convergence for L~p-mixingales are studied.Sufficient conditions are given for the complete moment convergence for the maximal partial sums of B-valued L~p-mixingales by utilizing the Rosenthal maximal type inequality for B-valued martingale difference sequence, which extend and improve the related known works in the literature.
