کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4615455 | 1339317 | 2015 | 8 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A multiplier condition for hypoellipticity of complex vector fields with optimal loss of derivatives
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
In CzÃRt we consider the function g=g(z), set g1=âzg, g11¯=âzâ¯zg and define the operator Lg=âz+ig1ât. We discuss estimates with loss of derivatives, in the sense of Kohn, for the system (L¯g,fkLg) where (L¯g,Lg) is 12m subelliptic at 0 and f(0)=0, df(0)â 0. We prove estimates with a loss l=kâ12m if the “multiplier” condition |f|â³|g11¯|12(mâ1) is fulfilled. (For estimates without cut-off, subellipticity can be weakened to compactness and this results in a loss of l=k2(mâ1).) For the choice (g,fk)=(|z|2m,z¯k) this result was obtained by Kohn and Bove-Derridj-Kohn-Tartakoff for m=1 and mâ¥1 respectively. Also, the loss l=kâ12m was proven to be optimal. We show that it remains optimal for the model (g,fk)=(x2m,xk). Instead, for the model (g,fk)=(|z|2m,xk), in which the multiplier condition is violated, the loss is not lowered by the type and must be â¥kâ12.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 423, Issue 1, 1 March 2015, Pages 318-325
Journal: Journal of Mathematical Analysis and Applications - Volume 423, Issue 1, 1 March 2015, Pages 318-325
نویسندگان
Luca Baracco,