Operator integral Hardy yang bekerja pada ruang fungsi Banach

HADIANNUR, Achyad, Dr. Supama, M.Si

2009 | Tesis | S2 Matematika

Selain memuat sifat-sifat pemetaan, seperti : keterbatasan (boundedness), kekompakan (compactness) operator integral Hardy (Hardy type integral operator) yang berkerja pada ruang fungsi Banach (Banach function space), tulisan ini juga memuat estimasi ukuran ketidakkompakan operator tersebut. Operator integral Hardy yang dibicarakan di dalam tulisan ini dilengkapi kernel Onairov (Onairov’s kernel), sedangkan ruang fungsi Banach dimana operator itu berkerja memenuhi syarat "simbol" - Berezhnoi ( "simbol" -Berezhnoi condition). Hasil penelitian pertama berupa syarat cukup dan syarat perlu agar operator integral Hardy terbatas. Berangkat dari hasil tersebut, diberikan syarat cukup dan perlu agar operator tersebut kompak dan juga diberikan estimasi ukuran ketidakkompakan operator integral Hardy.

In this paper, characterization of the mapping properties such as boundedness, compactness as well as measure of non-compactness of Hardy type integral operators acting on Banach fuction spaces are presented. The paper is devoted to Hardy type integral operators with Onairov’s kernel on Banach fuction spaces which satisfy "symbol" -Berezhnoi condition. Our first result characterizes the boundedness of the operators with Onairov’s kernel. This leads to a characterization of their compactness and measure of non-compactness.

Kata Kunci : Keterbatasan (boundedness),Intergral Hardy,Ruang Banach,Kernel Onairov,l,Berezhnoi