The monotoneity properties of certain functions defined in terms of the η-distortion function ηK(t) in quasiconformal theory are studied and asymptotically sharp bounds are obtained for ηK(t), thus proving some pro...The monotoneity properties of certain functions defined in terms of the η-distortion function ηK(t) in quasiconformal theory are studied and asymptotically sharp bounds are obtained for ηK(t), thus proving some properties of the upper bound function K(t, r) in Schottky’s theorem on analytic functions and improving the known explicit bounds for K( t, r ).展开更多
In this paper,it is proved that the Mori constant,the Hlder coeflicient of the family QC<sub>K</sub>（B）of K-quasiconformal self-mappings of the unit disk B with the origin fixed,is at most 46<sup>1...In this paper,it is proved that the Mori constant,the Hlder coeflicient of the family QC<sub>K</sub>（B）of K-quasiconformal self-mappings of the unit disk B with the origin fixed,is at most 46<sup>1-1/K</sup>.It is also shown that the Hlder coefficient of the restriction of a map f∈QC<sub>K</sub>（B）to the disk|z|≤sin 25.7°is at most 16<sup>1-1/K</sup>.展开更多
文摘The monotoneity properties of certain functions defined in terms of the η-distortion function ηK(t) in quasiconformal theory are studied and asymptotically sharp bounds are obtained for ηK(t), thus proving some properties of the upper bound function K(t, r) in Schottky’s theorem on analytic functions and improving the known explicit bounds for K( t, r ).
文摘In this paper,it is proved that the Mori constant,the Hlder coeflicient of the family QC<sub>K</sub>（B）of K-quasiconformal self-mappings of the unit disk B with the origin fixed,is at most 46<sup>1-1/K</sup>.It is also shown that the Hlder coefficient of the restriction of a map f∈QC<sub>K</sub>（B）to the disk|z|≤sin 25.7°is at most 16<sup>1-1/K</sup>.
