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On the almost sure boundedness of norms of some empirical operators

✍ Scribed by Rafał Latała

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
177 KB
Volume
38
Category
Article
ISSN
0167-7152

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✦ Synopsis

Let X~,X2 .... be /.i.d. random variables and h be a symmetric measurable real function. We show that the norms of operators on l~ given by the matrix (~h(Xi, X/)6i~i)l<i,i_<, are a.s. bounded if and only if h is square integrable.

📜 SIMILAR VOLUMES

On the boundedness of some potential-typ
On the boundedness of some potential-type operators with oscillating kernels
✍ Denis N. Karasev; Vladimir A. Nogin 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 282 KB

## Abstract We consider a class of multidimensional potential‐type operators with kernels that have singularities at the origin and on the unit sphere and that are oscillating at infinity. We describe some convex sets in the (1/__p,__ 1/__q__)‐plane for which these operators are bounded from __L~p~