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Orlicz_Hardy Inequalities
, M.Sc. Thesis Sharif University of Technology ; Ranjbar Motlagh, Alireza (Supervisor)
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
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