کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4607442 | 1337857 | 2012 | 12 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Sharp integral inequalities for fractional derivatives of trigonometric polynomials
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Sharp integral inequalities for fractional derivatives of trigonometric polynomials Sharp integral inequalities for fractional derivatives of trigonometric polynomials](/preview/png/4607442.png)
چکیده انگلیسی
We study sharp estimates of integral functionals for operators on the set Tn of real trigonometric polynomials fn of degree nâ¥1 in terms of the uniform norm âfnâC2Ï of the polynomials and similar questions for algebraic polynomials on the unit circle of the complex plane. P. Erdös, A.P. Calderon, G. Klein, L.V. Taikov, and others investigated such inequalities. In this paper, we, in particular, show that the sharp inequality âDαfnâqâ¤nαâcostâqâfnââ holds on the set Tn for the Weyl fractional derivatives Dαfn of order αâ¥1 for 0â¤q<â. For q=â (αâ¥1), this fact was proved by Lizorkin (1965) [12]. For 1â¤q<â and positive integer α, the inequality was proved by Taikov (1965) [23]; however, in this case, the inequality follows from results of an earlier paper by Calderon and Klein (1951) [6].
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Approximation Theory - Volume 164, Issue 11, November 2012, Pages 1501-1512
Journal: Journal of Approximation Theory - Volume 164, Issue 11, November 2012, Pages 1501-1512
نویسندگان
Vitalii V. Arestov, Polina Yu. Glazyrina,