Orlicz_Hardy Inequalities

Please enable javascript in your browser.

Soleimani Morche Khorti, Maryam | 2011

424 Viewed

Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 41714 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Ranjbar Motlagh, Alireza
Abstract:
The main purpose of this thesis is to establish the relationship between Orlicz-Hardy inequalities on a bounded Euclidean domain to certain fatness conditions on the comple-ment. Suppose Rn is a bounded domain and let d(x) := dist(x; @). We consider integral Hardy inequalities 8u 2 C1
0 ( ) Z ju(x)jd(x) C Z (jru(x)j)dxand norm Hardy inequalities8u 2 C1
0 () ju(x)jd(x) Cjkru(x)kj where : [0;1) ! [0;1) is a Young function and jk kj is representation of Luxemburg norm. Also the concept of fatness is introduced by concept of capacity
Keywords:
Potential ; Capacity ; Orlicz Spaces ; Orlicz-Hardy Inequalities ; Fatness

No TOC