Eigenvalue distribution of integral operators defined by Sobolev-Orlicz kernels .
Maamoun A. E. Faragallah ';
Abstract
In this introductory chapter we summarize some well known defini tions and explain certain terminology used throughout this thesis.Also this chapter contains the definition and elementary properties of the
Lorentz-sequence spaces lp,q,the Besov spaces B;,., the Sobolev spaces
w;, the Orlicz spaces Lif> and the (p, q)-summing operators Ilv,q• Fur
ther, the s-numbers of operators in Besov spaces is contained.
We use standard notations: N, Z, IR and 1C for the natural, integer, real and complex numbers respectively.We let N0 = N U {O}.The Ba nach spaces will be abbreviated by X,Y, Z and sometime by A, B.By operators we mean continuous linear operators between Banach spaces. The space of continuous linear operators T from X to Y under the operator norm:
Lorentz-sequence spaces lp,q,the Besov spaces B;,., the Sobolev spaces
w;, the Orlicz spaces Lif> and the (p, q)-summing operators Ilv,q• Fur
ther, the s-numbers of operators in Besov spaces is contained.
We use standard notations: N, Z, IR and 1C for the natural, integer, real and complex numbers respectively.We let N0 = N U {O}.The Ba nach spaces will be abbreviated by X,Y, Z and sometime by A, B.By operators we mean continuous linear operators between Banach spaces. The space of continuous linear operators T from X to Y under the operator norm:
Other data
| Title | Eigenvalue distribution of integral operators defined by Sobolev-Orlicz kernels . | Other Titles | توزيع القيم الذاتية للمؤثرات التكاملية المعرفة بواسطة نواه اورليتش - سوبوليف | Authors | Maamoun A. E. Faragallah ' | Issue Date | 1996 |
Attached Files
| File | Size | Format | |
|---|---|---|---|
| مأمون عبد الرازق فرج.pdf | 1.24 MB | Adobe PDF | View/Open |
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