Norm inequalities for integral operators on cones

منو

" Norm inequalities for integral operators on cones "
M. V. Siadat

Document Type	:	Latin Dissertation
Language of Document	:	English
Record Number	:	1112506
Doc. No	:	TLpq303900399
Main Entry	:	M. V. Siadat
Title & Author	:	Norm inequalities for integral operators on cones\ M. V. Siadat
College	:	University of Illinois at Chicago
Date	:	1990
student score	:	1990
Degree	:	Ph.D.
Page No	:	52
Abstract	:	This dissertation consists of two parts. (1) A review of properties of general homogeneous convex cones in usdR\sp{n}usd. (2) Norm inequalities for certain integral operators on such domains. For a special class of integral operators K, Kf(x) = usd\int\sb{V}k(x,y)f(y)dyusd, defined on a homogeneous convex con V, we obtain the following weighted (usdL\sp{p}usd, usdL\sp{q}usd) norm inequality: (1 usd\leq p\leq q\leq\inftyusd) usdusd\left(\int\sb{V} \Delta\sbsp{V}{\gamma - q} (x)(Kf(x))\sp{q} dx\right)\sp{\sp{1/q}}{\le}c\left(\int\sb{V} f\sp{p} (x) \Delta\sbsp{V}{\beta p + (\gamma + 1) p/q - 1} (x)dx\right)\sp{\sp{1/p}}usdusdwhere usd\Delta\sbsp{V}{\delta}(x)usd, the usdR\sp{n}usd analogue of usdx\sp{\delta}usd, is a special weight function. We then proceed to apply the above result and others to some important special operators and their duals. These operators are: Riemann-Liouville's, Weyl's and Laplace's. Hardy's operator and its dual are special cases of Riemann-Liouville's and Weyl's.
Subject	:	Mathematics
	:	Pure sciences