کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6417439 | 1339290 | 2016 | 28 صفحه PDF | دانلود رایگان |
We define Hardy spaces Hp(Dβâ²), pâ(1,â), on the non-smooth worm domain Dβâ²={(z1,z2)âC2:|Imz1âlogâ¡|z2|2|<Ï2,|logâ¡|z2|2|<βâÏ2} and we prove a series of related results such as the existence of boundary values on the distinguished boundary âDβⲠof the domain and a Fatou-type theorem (i.e., pointwise convergence to the boundary values). Thus, we study the SzegÅ projection operator SË and the associated SzegÅ kernel KDβâ². More precisely, if Hp(âDβâ²) denotes the space of functions which are boundary values for functions in Hp(Dβâ²), we prove that the operator SË extends to a bounded linear operatorSË:Lp(âDβâ²)âHp(âDβâ²) for every pâ(1,+â) andSË:Wk,p(âDβâ²)âWk,p(âDβâ²) for every k>0. Here Wk,p denotes the Sobolev space of order k and underlying Lp norm, pâ(1,â). As a consequence of the Lp boundedness of SË, we prove that Hp(Dβâ²)â©C(Dβâ²â¾) is a dense subspace of Hp(Dβâ²).
Journal: Journal of Mathematical Analysis and Applications - Volume 436, Issue 1, 1 April 2016, Pages 439-466