کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5775220 | 1413578 | 2017 | 19 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Orlicz spaces bounds for special classes of hyperbolic sums
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
Let R=R1Ãâ¯ÃRd denote a dyadic rectangle in the unit cube [0,1]d, dâ¥3. Let hR be the Lâ-normalized Haar function supported on R. In [10], the conjectured signed small ball inequality,ââ|R|=2ânαRhRâââ³nd2,whereαRâ{±1}, was proven under the additional assumption that the coefficients also satisfy the splitting property, αR=αR1â
αR2Ãâ¯ÃRd with αR1,αR2Ãâ¯ÃRdâ{±1}. We give another proof of this result, using a duality argument. Based on this approach, we also showââ|R|=2ânαRhRâexpâ¡(La)â³nd2â1a,2â¤a<â for any integer nâ¥1 and any choice of coefficients {αR}â{â1,1} which satisfy the splitting property. The above inequality has been conjectured for general coefficients αRâ{â1,1} in dâ¥3. These bounds are investigated further for more general coefficients {αR}â{â1,1}. The proof of the sharpness of the Lâ-lower bound of hyperbolic sums with coefficients satisfying the “splitting property” is also provided.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 449, Issue 2, 15 May 2017, Pages 1302-1320
Journal: Journal of Mathematical Analysis and Applications - Volume 449, Issue 2, 15 May 2017, Pages 1302-1320
نویسندگان
Dimitrios Karslidis,