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
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Orlicz spaces bounds for special classes of hyperbolic sums
چکیده انگلیسی
Let R=R1×⋯×Rd denote a dyadic rectangle in the unit cube [0,1]d, d≥3. Let hR be the L∞-normalized Haar function supported on R. In [10], the conjectured signed small ball inequality,‖∑|R|=2−nαRhR‖∞≳nd2,whereαR∈{±1}, was proven under the additional assumption that the coefficients also satisfy the splitting property, αR=αR1⋅αR2×⋯×Rd with αR1,αR2×⋯×Rd∈{±1}. We give another proof of this result, using a duality argument. Based on this approach, we also show‖∑|R|=2−nαRhR‖exp⁡(La)≳nd2−1a,2≤a<∞ for any integer n≥1 and any choice of coefficients {αR}⊂{−1,1} which satisfy the splitting property. The above inequality has been conjectured for general coefficients αR∈{−1,1} in d≥3. These bounds are investigated further for more general coefficients {αR}⊂{−1,1}. The proof of the sharpness of the L∞-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
نویسندگان
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