A Growth Behavior of SzegöType Operators  

作　　者：Jongho Yang Jongho Yang(Department of Mathematics Education, Korea National University of Education, Chungbuk, Korea)

机构地区：[1]Department of Mathematics Education, Korea National University of Education, Chungbuk, Korea

出　　处：《Advances in Pure Mathematics》2020年第9期492-500,共9页理论数学进展（英文）

摘　　要：We define new integral operators on the Haydy space similar to Szeg<span style="white-space:nowrap;"><span style="white-space:nowrap;">&#246;</span></span><span style="font-family:Verdana;"> projection. We show that these operators map from </span><i><span style="font-family:Verdana;">H^{<i style="white-space:normal;"><span style="font-family:Verdana;">p</span></i>}</span></i><i><span style="font-family:Verdana;"> </span></i><span style="font-family:Verdana;">to </span><i><span style="font-family:Verdana;">H</span></i><span style="font-family:Verdana;">^{<span style="white-space:normal;font-family:Verdana;">2 </span>}</span><span style="font-family:Verdana;">for some 1 </span><i><span style="font-family:Verdana;">≤ </span></i><i><span style="font-family:Verdana;">p < </span></i><span style="font-family:Verdana;">2, where the range of </span><i><span style="font-family:Verdana;">p </span></i><span style="font-family:CMR10;"><span style="font-family:Verdana;">is depending on a growth condition. To prove that, we generalize the Hausdorff-Young Theorem to multi-dimensional case.</span></span>We define new integral operators on the Haydy space similar to Szeg<span style="white-space:nowrap;"><span style="white-space:nowrap;">&#246;</span></span><span style="font-family:Verdana;"> projection. We show that these operators map from </span><i><span style="font-family:Verdana;">H^{<i style="white-space:normal;"><span style="font-family:Verdana;">p</span></i>}</span></i><i><span style="font-family:Verdana;"> </span></i><span style="font-family:Verdana;">to </span><i><span style="font-family:Verdana;">H</span></i><span style="font-family:Verdana;">^{<span style="white-space:normal;font-family:Verdana;">2 </span>}</span><span style="font-family:Verdana;">for some 1 </span><i><span style="font-family:Verdana;">≤ </span></i><i><span style="font-family:Verdana;">p < </span></i><span style="font-family:Verdana;">2, where the range of </span><i><span style="font-family:Verdana;">p </span></i><span style="font-family:CMR10;"><span style="font-family:Verdana;">is depending on a growth condition. To prove that, we generalize the Hausdorff-Young Theorem to multi-dimensional case.</span></span>

关 键 词：Szegö Projection Hausdorff-Young Theorem Coeffcient Multiplier Stein Interpolation Theorem 

分 类 号：O17[理学—数学]