This book offers a unified framework for the analysis of function spaces associated with non-additive measures. Motivated by questions arising in nonlinear potential theory and super-critical PDEs, it develops the calculus of Choquet integration and studies the structural properties of Lorentz-type spaces defined via general capacities. Particular attention is given to Bessel capacities, including their role in describing fine properties of Sobolev functions and the normability of Choquet integral spaces. Building on this foundation, the second part introduces and characterizes Sobolev multiplier spaces defined through capacities, establishing their preduals and embedding properties. The boundedness of maximal operators is analyzed using tools from nonlinear potential theory, yielding vector-valued estimates in this setting. The monograph is intended for researchers in analysis and PDEs interested in the interplay between capacity theory, function spaces, and operator estimates.
eBook - PDF
Capacitary Calculus
With Special Attention to Sobolev Multiplier Spaces and Their Preduals
- 213 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
Capacitary Calculus
With Special Attention to Sobolev Multiplier Spaces and Their Preduals
About this book
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Information
Publisher
De GruyterEdition
1Year
2026Topic
MathematicsPrint ISBN
9783112242322
Subtopic
Mathematical AnalysiseBook ISBN
9783112242339
Index
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Yes, you can access Capacitary Calculus by Keng Hao Ooi in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematical Analysis. We have over 1.5 million books available in our catalogue for you to explore.