کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5775136 | 1413576 | 2017 | 6 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Ramsey-type theorems for sets satisfying a geometric regularity condition
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We consider Ramsey-type problems associated to collections of sets in Rn satisfying a standard geometric regularity condition. In particular, let {Rj}j=1N be a collection of measurable sets in Rn such that every Rj is contained in a cube Qj whose sides are parallel to the axes and such that |Rj|/|Qj|â¥Ï>0. Moreover, suppose that there exists 0<γ<â such that |Rj|/|Rk|â¤Î³ for every j,k. We prove that there exists a subcollection of {Rj}j=1N consisting of at least R(N) sets that either have a point of common intersection or that are pairwise disjoint, where R(N)â¥(NÏ(1+2â
γ1/n)n)1/2. If the sets in the collection {Rj} are convex, we obtain the improved Ramsey estimate R(N)â¥(3ânÏN)1/2. Applications of these results to weak type bounds of geometric maximal operators are provided.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 447, Issue 2, 15 March 2017, Pages 951-956
Journal: Journal of Mathematical Analysis and Applications - Volume 447, Issue 2, 15 March 2017, Pages 951-956
نویسندگان
P. Hagelstein, D. Herden, D. Young,