In this paper,we mainly use the Frechet derivative to extend the Bohr inequality with a lacunary series to the higher-dimensional space,namely,mappings from Unto U(resp.Unto Un).In addition,we discuss whether or not t...In this paper,we mainly use the Frechet derivative to extend the Bohr inequality with a lacunary series to the higher-dimensional space,namely,mappings from Unto U(resp.Unto Un).In addition,we discuss whether or not there is a constant term in f,and we obtain two redefined Bohr inequalities in Un.Finally,we redefine the Bohr inequality of the odd and even terms of the analytic function f so as to obtain conclusions for two different higher-dimensional alternating series.展开更多
For Oppenheim series epansions, the authors of [7] discussed the exceptional sets Bm={x∈（0,1]：1〈dj（x）/h（j-1）（d（j-1）（x））≤m for any j ≥2} In this paper, we investigate the Hausdorff dimension of a kind o...For Oppenheim series epansions, the authors of [7] discussed the exceptional sets Bm={x∈（0,1]：1〈dj（x）/h（j-1）（d（j-1）（x））≤m for any j ≥2} In this paper, we investigate the Hausdorff dimension of a kind of exceptional sets occurring in alternating Oppenheim series expansion. As an application, we get the exact Hausdorff dimension of the-set in Luroth series expansion, also we give an estimate of such dimensional number.展开更多
The error-sum function of alternating Lǖroth series is introduced, which, to some extent, discerns the superior or not of an expansion comparing to other expansions. Some elementary properties of this function are st...The error-sum function of alternating Lǖroth series is introduced, which, to some extent, discerns the superior or not of an expansion comparing to other expansions. Some elementary properties of this function are studied. Also, the Hausdorff dimension of graph of such function is determined.展开更多
基金supported by Guangdong Natural Science Foundations(2021A1515010058)。
文摘In this paper,we mainly use the Frechet derivative to extend the Bohr inequality with a lacunary series to the higher-dimensional space,namely,mappings from Unto U(resp.Unto Un).In addition,we discuss whether or not there is a constant term in f,and we obtain two redefined Bohr inequalities in Un.Finally,we redefine the Bohr inequality of the odd and even terms of the analytic function f so as to obtain conclusions for two different higher-dimensional alternating series.
文摘For Oppenheim series epansions, the authors of [7] discussed the exceptional sets Bm={x∈（0,1]：1〈dj（x）/h（j-1）（d（j-1）（x））≤m for any j ≥2} In this paper, we investigate the Hausdorff dimension of a kind of exceptional sets occurring in alternating Oppenheim series expansion. As an application, we get the exact Hausdorff dimension of the-set in Luroth series expansion, also we give an estimate of such dimensional number.
文摘The error-sum function of alternating Lǖroth series is introduced, which, to some extent, discerns the superior or not of an expansion comparing to other expansions. Some elementary properties of this function are studied. Also, the Hausdorff dimension of graph of such function is determined.
