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9781470465759 Academic Inspection Copy

Maximal Function Methods for Sobolev Spaces

  • ISBN-13: 9781470465759
  • Publisher: AMERICAN MATHEMATICAL SOCIETY
    Imprint: AMERICAN MATHEMATICAL SOCIETY
  • By Juha Kinnunen, By Juha Lehrback, By Antti Vahakangas
  • Price: AUD $321.00
  • Stock: 0 in stock
  • Availability: This book is temporarily out of stock, order will be despatched as soon as fresh stock is received.
  • Local release date: 28/11/2022
  • Format: Paperback (254.00mm X 178.00mm) 354 pages Weight: 550g
  • Categories: Calculus [PBKA]
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This book discusses advances in maximal function methods related to Poincare and Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's inequalities, and partial differential equations. Capacities are needed for fine properties of Sobolev functions and characterization of Sobolev spaces with zero boundary values. The authors consider several uniform quantitative conditions that are self-improving, such as Hardy's inequalities, capacity density conditions, and reverse Hoelder inequalities. They also study Muckenhoupt weight properties of distance functions and combine these with weighted norm inequalities; notions of dimension are then used to characterize density conditions and to give sufficient and necessary conditions for Hardy's inequalities. At the end of the book, the theory of weak solutions to the p -Laplace equation and the use of maximal function techniques is this context are discussed. The book is directed to researchers and graduate students interested in applications of geometric and harmonic analysis in Sobolev spaces and partial differential equations.
Juha Kinnunen, Aalto University, Finland. Juha Lehrback, University of Jyvaskyla, Finland. Antti Vahakangas, University of Jyvaskyla, Finland.
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