Extremal Extensions from the Circle to the Disk
Extremal Extensions from the Circle to the Disk
复制标题
DOI：
10.1007/978-1-4612-0605-7_18
复制
发表时间：
1998
期刊：
影响因子：
--
通讯作者：
E. Reich
中科院分区：
文献类型：
--
作者：
E. Reich
Let$$ \Delta = \{ |z|{\rm{ }} < {\rm{1\} , }}\Gamma {\rm{ = \{ |}}z{\rm{| = 1\} , }}\partial {\rm{ = (}}\partial _x - i\partial _y )/2, \bar \partial = (\partial _x + i\partial _y )/2 $$ In this exposition we shall be concerned with two kinds of extension problems from, namely, firstly, theleast non-analytic(abbreviated LNA) extensions ofcontinuouscomplex-valued boundary values, and, secondly, theextremal quasiconformal(abbreviated EQC) extensions ofhomeomorphicboundary values. We formulate the first problem as follows. Let, be a continuous complex-valued function. It will often be convenient to normalizegby the conditions
Let$$ \Delta = \{ |z|{\rm{ }} < {\rm{1\} , }}\Gamma {\rm{ = \{ |}}z{\rm{| = 1\} , }}\partial {\rm{ = (}}\partial _x - i\partial _y )/2, \bar \partial = (\partial _x + i\partial _y )/2 $$ In this exposition we shall be concerned with two kinds of extension problems from, namely, firstly, theleast non-analytic(abbreviated LNA) extensions ofcontinuouscomplex-valued boundary values, and, secondly, theextremal quasiconformal(abbreviated EQC) extensions ofhomeomorphicboundary values. We formulate the first problem as follows. Let, be a continuous complex-valued function. It will often be convenient to normalizegby the conditions