کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6417439 1339290 2016 28 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Hardy spaces and the Szegő projection of the non-smooth worm domain Dβ′
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Hardy spaces and the Szegő projection of the non-smooth worm domain Dβ′
چکیده انگلیسی

We define Hardy spaces Hp(Dβ′), p∈(1,∞), on the non-smooth worm domain Dβ′={(z1,z2)∈C2:|Imz1−log⁡|z2|2|<π2,|log⁡|z2|2|<β−π2} and we prove a series of related results such as the existence of boundary values on the distinguished boundary ∂Dβ′ of the domain and a Fatou-type theorem (i.e., pointwise convergence to the boundary values). Thus, we study the Szegő projection operator S˜ and the associated Szegő kernel KDβ′. More precisely, if Hp(∂Dβ′) denotes the space of functions which are boundary values for functions in Hp(Dβ′), we prove that the operator S˜ extends to a bounded linear operatorS˜:Lp(∂Dβ′)→Hp(∂Dβ′) for every p∈(1,+∞) andS˜:Wk,p(∂Dβ′)→Wk,p(∂Dβ′) for every k>0. Here Wk,p denotes the Sobolev space of order k and underlying Lp norm, p∈(1,∞). As a consequence of the Lp boundedness of S˜, we prove that Hp(Dβ′)∩C(Dβ′‾) is a dense subspace of Hp(Dβ′).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 436, Issue 1, 1 April 2016, Pages 439-466
نویسندگان
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