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This monograph is the first one to systematically present a series
of local and global estimates and inequalities for differential
forms, in particular the ones that satisfy the A-harmonic
equations. The presentation focuses on the Hardy-Littlewood,
Poincare, Cacciooli, imbedded and reverse Holder inequalities.
Integral estimates for operators, such as homotopy operator, the
Laplace-Beltrami operator, and the gradient operator are discussed
next. Additionally, some related topics such as BMO inequalities,
Lipschitz classes, Orlicz spaces and inequalities in Carnot groups
are discussed in the concluding chapter. An abundance of
bibliographical references and historical material supplement the
text throughout. This rigorous presentation requires a familiarity
with topics such as differential forms, topology and Sobolev space
theory. It will serve as an invaluable reference for researchers,
instructors and graduate students in analysis and partial
differential equations and could be used as additional material for
specific courses in these fields.
Differential forms satisfying the A-harmonic equations have found
wide applications in fields such as general relativity, theory of
elasticity, quasiconformal analysis, differential geometry, and
nonlinear differential equations in domains on manifolds. This
monograph is the first one to systematically present a series of
local and global estimates and inequalities for such differential
forms in particular. It concentrates on the Hardy-Littlewood,
Poincare, Cacciooli, imbedded and reverse Holder inequalities.
Integral estimates for operators, such as homotopy operator, the
Laplace-Beltrami operator, and the gradient operator are also
presented. Additionally, some related topics such as BMO
inequalities, Lipschitz classes, Orlicz spaces and inequalities in
Carnot groups are discussed in the concluding chapter. An abundance
of bibliographical references and historical material supplement
the text throughout. This book will serve as an invaluable
reference for researchers, instructors and graduate students in
analysis and partial differential equations and could be used as
additional material for specific courses in these fields.
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