- Tytuł:
- Compactness of Hardy-type integral operators in weighted Banach function spaces
- Autorzy:
-
E. Edmunds, David
Gurka, Petr
Pick, Luboš - Powiązania:
- https://bibliotekanauki.pl/articles/1290637.pdf
- Data publikacji:
- 1994
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
weighted Banach function space
Hardy-type operator
compact operator
Lorentz space - Opis:
- We consider a generalized Hardy operator $Tf(x) = ϕ(x) ʃ_{0}^{x} ψfv$. For T to be bounded from a weighted Banach function space (X,v) into another, (Y,w), it is always necessary that the Muckenhoupt-type condition $ℬ = sup_{R>0} ∥ϕχ_{(R,∞)}∥_{Y}∥ψχ_{(0,R)}∥_{X'} < ∞$ be satisfied. We say that (X,Y) belongs to the category M(T) if this Muckenhoupt condition is also sufficient. We prove a general criterion for compactness of T from X to Y when (X,Y) ∈ M(T) and give an estimate for the distance of T from the finite rank operators. We apply the results to Lorentz spaces and characterize pairs of Lorentz spaces which fall into M (T).
- Źródło:
-
Studia Mathematica; 1994, 109, 1; 73-90
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł