2 results
CORRECTION TO ‘CHOQUET INTEGRALS, HAUSDORFF CONTENT AND FRACTIONAL OPERATORS’
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society , First View
- Published online by Cambridge University Press:
- 04 October 2024, pp. 1-3
-
- Article
-
- You have access
- HTML
- Export citation
CHOQUET INTEGRALS, HAUSDORFF CONTENT AND FRACTIONAL OPERATORS
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 110 / Issue 2 / October 2024
- Published online by Cambridge University Press:
- 19 March 2024, pp. 355-366
- Print publication:
- October 2024
-
- Article
-
- You have access
- HTML
- Export citation
-
We show that the fractional integral operator
$I_{\alpha }$, 
$0<\alpha <n$, and the fractional maximal operator 
$M_{\alpha }$, 
$0\le \alpha <n$, are bounded on weak Choquet spaces with respect to Hausdorff content. We also investigate these operators on Choquet–Morrey spaces. The results for the fractional maximal operator 
$M_\alpha $ are extensions of the work of Tang [‘Choquet integrals, weighted Hausdorff content and maximal operators’, Georgian Math. J. 18(3) (2011), 587–596] and earlier work of Adams and Orobitg and Verdera. The results for the fractional integral operator 
$I_{\alpha }$ are essentially new.
